Solving algebra with multiple square rootSolving Linear Systems with Arbitrary ConstantsSolving equations with multiple rootsSimple square-root calculation parsing /order of operationsHow to solve $y^2=3x^4+3x^2+1$ for integers.Solving inequality involving square root and division by logarithm: $sqrt n<fracnlog(n)-2$What is $Asetminus B$ Space?Solving an equation containing cube roots: $sqrt[3]5x+7-sqrt[3]5x-12=1$How do I solve $2(sqrt2+sqrt6)over3(sqrt2+sqrt3)$Cubic root epsilon delta proofEvaluate the determinant with Identity matrix
What does the "remote control" for a QF-4 look like?
Can a Cauchy sequence converge for one metric while not converging for another?
Why does Kotter return in Welcome Back Kotter?
infared filters v nd
Why "Having chlorophyll without photosynthesis is actually very dangerous" and "like living with a bomb"?
How to determine what difficulty is right for the game?
What defenses are there against being summoned by the Gate spell?
I'm flying to France today and my passport expires in less than 2 months
Can I make popcorn with any corn?
How is the claim "I am in New York only if I am in America" the same as "If I am in New York, then I am in America?
Revoked SSL certificate
What's the point of deactivating Num Lock on login screens?
Is it unprofessional to ask if a job posting on GlassDoor is real?
Can an x86 CPU running in real mode be considered to be basically an 8086 CPU?
Can you really stack all of this on an Opportunity Attack?
How to format long polynomial?
How can bays and straits be determined in a procedurally generated map?
LaTeX: Why are digits allowed in environments, but forbidden in commands?
How much of data wrangling is a data scientist's job?
Theorems that impeded progress
Add text to same line using sed
Important Resources for Dark Age Civilizations?
Malformed Address '10.10.21.08/24', must be X.X.X.X/NN or
RSA: Danger of using p to create q
Solving algebra with multiple square root
Solving Linear Systems with Arbitrary ConstantsSolving equations with multiple rootsSimple square-root calculation parsing /order of operationsHow to solve $y^2=3x^4+3x^2+1$ for integers.Solving inequality involving square root and division by logarithm: $sqrt n<fracnlog(n)-2$What is $Asetminus B$ Space?Solving an equation containing cube roots: $sqrt[3]5x+7-sqrt[3]5x-12=1$How do I solve $2(sqrt2+sqrt6)over3(sqrt2+sqrt3)$Cubic root epsilon delta proofEvaluate the determinant with Identity matrix
$begingroup$
I am currently solving an algebra and can't figure it out, could anyone help me on this?
$$2sqrtN + sqrtN^2+4c^2 = sqrtN + sqrtN^2+3c^2 + sqrtN + sqrtN^2+5c^2$$
Which I would like to have a solution to represent N in terms of c, or c in terms of N, either way works. If this is unsolvable, please show me the reason for that.
Thanks in advance.
linear-algebra diophantine-equations radicals
asked Mar 21 at 18:44
PetaGlzPetaGlz
124
$endgroup$
|
show 2 more comments
$begingroup$
I am currently solving an algebra and can't figure it out, could anyone help me on this?
$$2sqrtN + sqrtN^2+4c^2 = sqrtN + sqrtN^2+3c^2 + sqrtN + sqrtN^2+5c^2$$
Which I would like to have a solution to represent N in terms of c, or c in terms of N, either way works. If this is unsolvable, please show me the reason for that.
Thanks in advance.
linear-algebra diophantine-equations radicals
asked Mar 21 at 18:44
PetaGlzPetaGlz
124
$endgroup$
$begingroup$
Do you have values for the variable $c$ ?
$endgroup$
– Dr. Sonnhard Graubner
Mar 21 at 18:53
$begingroup$
The solution of Maple is a polynomial of degree 64!
$endgroup$
– Dr. Sonnhard Graubner
Mar 21 at 18:55
$begingroup$
hey Dr! both N and c are positive integers! So does that mean this is unsolvable?
$endgroup$
– PetaGlz
Mar 21 at 18:58
$begingroup$
It is solvable, but i think no per hand!
$endgroup$
– Dr. Sonnhard Graubner
Mar 21 at 18:59
$begingroup$
@Dr.SonnhardGraubner ok...so could u show me some possible approaches?
$endgroup$
– PetaGlz
Mar 21 at 19:00
|
show 2 more comments
$begingroup$
I am currently solving an algebra and can't figure it out, could anyone help me on this?
$$2sqrtN + sqrtN^2+4c^2 = sqrtN + sqrtN^2+3c^2 + sqrtN + sqrtN^2+5c^2$$
Which I would like to have a solution to represent N in terms of c, or c in terms of N, either way works. If this is unsolvable, please show me the reason for that.
Thanks in advance.
linear-algebra diophantine-equations radicals
asked Mar 21 at 18:44
PetaGlzPetaGlz
124
$endgroup$
I am currently solving an algebra and can't figure it out, could anyone help me on this?
$$2sqrtN + sqrtN^2+4c^2 = sqrtN + sqrtN^2+3c^2 + sqrtN + sqrtN^2+5c^2$$
Which I would like to have a solution to represent N in terms of c, or c in terms of N, either way works. If this is unsolvable, please show me the reason for that.
Thanks in advance.
linear-algebra diophantine-equations radicals
linear-algebra diophantine-equations radicals
asked Mar 21 at 18:44
PetaGlzPetaGlz
124
asked Mar 21 at 18:44
PetaGlzPetaGlz
124
asked Mar 21 at 18:44
PetaGlzPetaGlz
124
asked Mar 21 at 18:44
PetaGlzPetaGlz
124
asked Mar 21 at 18:44
PetaGlzPetaGlz
124
124
$begingroup$
Do you have values for the variable $c$ ?
$endgroup$
– Dr. Sonnhard Graubner
Mar 21 at 18:53
$begingroup$
The solution of Maple is a polynomial of degree 64!
$endgroup$
– Dr. Sonnhard Graubner
Mar 21 at 18:55
$begingroup$
hey Dr! both N and c are positive integers! So does that mean this is unsolvable?
$endgroup$
– PetaGlz
Mar 21 at 18:58
$begingroup$
It is solvable, but i think no per hand!
$endgroup$
– Dr. Sonnhard Graubner
Mar 21 at 18:59
$begingroup$
@Dr.SonnhardGraubner ok...so could u show me some possible approaches?
$endgroup$
– PetaGlz
Mar 21 at 19:00
|
show 2 more comments
$begingroup$
Do you have values for the variable $c$ ?
$endgroup$
– Dr. Sonnhard Graubner
Mar 21 at 18:53
$begingroup$
The solution of Maple is a polynomial of degree 64!
$endgroup$
– Dr. Sonnhard Graubner
Mar 21 at 18:55
$begingroup$
hey Dr! both N and c are positive integers! So does that mean this is unsolvable?
$endgroup$
– PetaGlz
Mar 21 at 18:58
$begingroup$
It is solvable, but i think no per hand!
$endgroup$
– Dr. Sonnhard Graubner
Mar 21 at 18:59
$begingroup$
@Dr.SonnhardGraubner ok...so could u show me some possible approaches?
$endgroup$
– PetaGlz
Mar 21 at 19:00
$begingroup$
Do you have values for the variable $c$ ?
$endgroup$
– Dr. Sonnhard Graubner
Mar 21 at 18:53
$begingroup$
Do you have values for the variable $c$ ?
$endgroup$
– Dr. Sonnhard Graubner
Mar 21 at 18:53
$begingroup$
The solution of Maple is a polynomial of degree 64!
$endgroup$
– Dr. Sonnhard Graubner
Mar 21 at 18:55
$begingroup$
The solution of Maple is a polynomial of degree 64!
$endgroup$
– Dr. Sonnhard Graubner
Mar 21 at 18:55
$begingroup$
hey Dr! both N and c are positive integers! So does that mean this is unsolvable?
$endgroup$
– PetaGlz
Mar 21 at 18:58
$begingroup$
hey Dr! both N and c are positive integers! So does that mean this is unsolvable?
$endgroup$
– PetaGlz
Mar 21 at 18:58
$begingroup$
It is solvable, but i think no per hand!
$endgroup$
– Dr. Sonnhard Graubner
Mar 21 at 18:59
$begingroup$
It is solvable, but i think no per hand!
$endgroup$
– Dr. Sonnhard Graubner
Mar 21 at 18:59
$begingroup$
@Dr.SonnhardGraubner ok...so could u show me some possible approaches?
$endgroup$
– PetaGlz
Mar 21 at 19:00
$begingroup$
@Dr.SonnhardGraubner ok...so could u show me some possible approaches?
$endgroup$
– PetaGlz
Mar 21 at 19:00
|
show 2 more comments
1 Answer
1
active
oldest
votes
$begingroup$
Of course $c=0$ is a solution. But there are no other real solutions.
After noting that $N=0$ is impossible, we divide both sides by $sqrtN$ and let $c^2/N^2 = t$ to get
$$ 2 sqrt1+sqrt1 + 4 t = sqrt1+sqrt1+3t + sqrt1+sqrt1+5t $$
We can write this as
$$ 2 g(4 t) = g(3 t) + g(5 t) $$
where
$$ g(x) = sqrt1+sqrt1+x$$
Now this function is strictly concave for $x > 0$, as we see by taking its second derivative. Thus since $4 = (3+5)/2$, $g(4t) > (g(3t) + g(5t))/2$ for $t > 0$.
answered Mar 21 at 19:22
Robert IsraelRobert Israel
330k23219473
$endgroup$
1
$begingroup$
That is very clear and fast. Thanks a lot!
$endgroup$
– PetaGlz
Mar 21 at 19:32
add a comment |
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3157229%2fsolving-algebra-with-multiple-square-root%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Of course $c=0$ is a solution. But there are no other real solutions.
After noting that $N=0$ is impossible, we divide both sides by $sqrtN$ and let $c^2/N^2 = t$ to get
$$ 2 sqrt1+sqrt1 + 4 t = sqrt1+sqrt1+3t + sqrt1+sqrt1+5t $$
We can write this as
$$ 2 g(4 t) = g(3 t) + g(5 t) $$
where
$$ g(x) = sqrt1+sqrt1+x$$
Now this function is strictly concave for $x > 0$, as we see by taking its second derivative. Thus since $4 = (3+5)/2$, $g(4t) > (g(3t) + g(5t))/2$ for $t > 0$.
answered Mar 21 at 19:22
Robert IsraelRobert Israel
330k23219473
$endgroup$
1
$begingroup$
That is very clear and fast. Thanks a lot!
$endgroup$
– PetaGlz
Mar 21 at 19:32
add a comment |
$begingroup$
Of course $c=0$ is a solution. But there are no other real solutions.
After noting that $N=0$ is impossible, we divide both sides by $sqrtN$ and let $c^2/N^2 = t$ to get
$$ 2 sqrt1+sqrt1 + 4 t = sqrt1+sqrt1+3t + sqrt1+sqrt1+5t $$
We can write this as
$$ 2 g(4 t) = g(3 t) + g(5 t) $$
where
$$ g(x) = sqrt1+sqrt1+x$$
Now this function is strictly concave for $x > 0$, as we see by taking its second derivative. Thus since $4 = (3+5)/2$, $g(4t) > (g(3t) + g(5t))/2$ for $t > 0$.
answered Mar 21 at 19:22
Robert IsraelRobert Israel
330k23219473
$endgroup$
1
$begingroup$
That is very clear and fast. Thanks a lot!
$endgroup$
– PetaGlz
Mar 21 at 19:32
add a comment |
$begingroup$
Of course $c=0$ is a solution. But there are no other real solutions.
After noting that $N=0$ is impossible, we divide both sides by $sqrtN$ and let $c^2/N^2 = t$ to get
$$ 2 sqrt1+sqrt1 + 4 t = sqrt1+sqrt1+3t + sqrt1+sqrt1+5t $$
We can write this as
$$ 2 g(4 t) = g(3 t) + g(5 t) $$
where
$$ g(x) = sqrt1+sqrt1+x$$
Now this function is strictly concave for $x > 0$, as we see by taking its second derivative. Thus since $4 = (3+5)/2$, $g(4t) > (g(3t) + g(5t))/2$ for $t > 0$.
answered Mar 21 at 19:22
Robert IsraelRobert Israel
330k23219473
$endgroup$
Of course $c=0$ is a solution. But there are no other real solutions.
After noting that $N=0$ is impossible, we divide both sides by $sqrtN$ and let $c^2/N^2 = t$ to get
$$ 2 sqrt1+sqrt1 + 4 t = sqrt1+sqrt1+3t + sqrt1+sqrt1+5t $$
We can write this as
$$ 2 g(4 t) = g(3 t) + g(5 t) $$
where
$$ g(x) = sqrt1+sqrt1+x$$
Now this function is strictly concave for $x > 0$, as we see by taking its second derivative. Thus since $4 = (3+5)/2$, $g(4t) > (g(3t) + g(5t))/2$ for $t > 0$.
answered Mar 21 at 19:22
Robert IsraelRobert Israel
330k23219473
answered Mar 21 at 19:22
Robert IsraelRobert Israel
330k23219473
answered Mar 21 at 19:22
Robert IsraelRobert Israel
330k23219473
answered Mar 21 at 19:22
Robert IsraelRobert Israel
330k23219473
330k23219473
1
$begingroup$
That is very clear and fast. Thanks a lot!
$endgroup$
– PetaGlz
Mar 21 at 19:32
add a comment |
1
$begingroup$
That is very clear and fast. Thanks a lot!
$endgroup$
– PetaGlz
Mar 21 at 19:32
1
1
$begingroup$
That is very clear and fast. Thanks a lot!
$endgroup$
– PetaGlz
Mar 21 at 19:32
$begingroup$
That is very clear and fast. Thanks a lot!
$endgroup$
– PetaGlz
Mar 21 at 19:32
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3157229%2fsolving-algebra-with-multiple-square-root%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
Do you have values for the variable $c$ ?
$endgroup$
– Dr. Sonnhard Graubner
Mar 21 at 18:53
$begingroup$
The solution of Maple is a polynomial of degree 64!
$endgroup$
– Dr. Sonnhard Graubner
Mar 21 at 18:55
$begingroup$
hey Dr! both N and c are positive integers! So does that mean this is unsolvable?
$endgroup$
– PetaGlz
Mar 21 at 18:58
$begingroup$
It is solvable, but i think no per hand!
$endgroup$
– Dr. Sonnhard Graubner
Mar 21 at 18:59
$begingroup$
@Dr.SonnhardGraubner ok...so could u show me some possible approaches?
$endgroup$
– PetaGlz
Mar 21 at 19:00