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Find the positive constants a and b such that x^4 + 9/x^4 = (x^2 - a/(x^2))^2 + b for all non zero values of x.

Damn!!!!! help.

Reply 1

Kvothe the Arcane

Original post by Dines

Find the positive constants a and b such that x^4 + 9/x^4 = (x^2 - a/(x^2))^2 + b for all non zero values of x.

Damn!!!!! help.

Is that

x^4 + \dfrac{9}{x^4} = \left(x^2 - \dfrac{a}{x^2} \right)^2 + b

?

Expand and compare coefficients.

Reply 2

Dines

Original post by Kvothe the arcane

Is that

x^4 + \dfrac{9}{x^4} = \left(x^2 - \dfrac{a}{x^2} \right)^2 + b

?

Expand and compare coefficients.

You there? How to expand. Just give me a starting hint.

(edited 8 years ago)

Reply 3

Kvothe the Arcane

Original post by Dines

You there? How to expand. Just give me a starting hint.

Expand the bracket as you would normally.

(\lambda-\mu)^2=\lambda^2-2 \lambda \mu + \mu^2

.
Except in this case,

\lambda=x^2

and

\mu=\dfrac{a}{x^2}

(edited 8 years ago)

Reply 4

KaylaB

Original post by Dines

How to expand this

If you know how to expand brackets normally, then this is no different, if not see below

Spoiler

if it makes it easier say that u=a/x^2
So then you would need to expand (x^2 -y)
Then you can just substitute in the value of u later on :h:

Reply 5

thefatone

Original post by Kvothe the arcane

Expand the bracket as you would normally.

(\lambda-\mu)^2=\lambda^2-2 \lambda \mu + \mu^2

.
Except in this case,

\lambda=x^2

and

\mu=\dfrac{a}{x^2}

Wouldn't that be

\dfrac {a^2}{x^4}

(edited 8 years ago)

Reply 6

KaylaB

Original post by Kvothe the arcane

Expand the bracket as you would normally.

(\lambda-\mu)^2=\lambda^2-2 \lambda \mu + \mu^2

.
Except in this case,

\lambda=x^2

and

\mu=\dfrac{a}{x^2}

Mu should be a/x^2 :tongue:

(edited 8 years ago)

Reply 7

Kvothe the Arcane

Original post by thefatone

Wouldn't that be

Spoiler

(edited 8 years ago)

Reply 8

thefatone

Original post by Kvothe the arcane

Spoiler

lol you edit mine aswell xD

guess i should put in a spoiler xD

Reply 9

Dines

I gained the answer.
a=3
b=6

Thank you.

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