If x-3/x=sqrt(3) then 9/(x^4)+(x^4)/9 = ? I got 7

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
Chasyesker
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If x-3/x=sqrt(3) then 9/(x^4)+(x^4)/9 = ? I got 7

Postby Chasyesker » Wed Sep 25, 2013 7:13 pm

If x-3/x=sqrt(3) then 9/(x^4)+(x^4)/9 = ?

I got the answer as 7 with both a calculator and in exact closed form using quadratic formula but my son's teacher says there is a way to rearrange the equations to get the answer w/o actually solving for x. I have my doubts. Can anyone see how to do it w/o solving for x first?

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maggiemagnet
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Re: If x-3/x=sqrt(3) then 9/(x^4)+(x^4)/9 = ? I got 7

Postby maggiemagnet » Wed Sep 25, 2013 9:27 pm

Chasyesker wrote:If x-3/x=sqrt(3) then 9/(x^4)+(x^4)/9 = ?

I got the answer as 7 with both a calculator and in exact closed form using quadratic formula but my son's teacher says there is a way to rearrange the equations to get the answer w/o actually solving for x. I have my doubts. Can anyone see how to do it w/o solving for x first?

There's a trick that may seem "obvious" after you've seen it, but hardly anybody thinks it up on their own. Tell your son to try squaring both sides of the "given", and adding 6 to both sides. Then square again, and subtract the 18 from both sides. Then divide through by 9 and see what he has.
:clap:

Chasyesker
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Joined: Wed Sep 25, 2013 7:04 pm
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Re: If x-3/x=sqrt(3) then 9/(x^4)+(x^4)/9 = ? I got 7

Postby Chasyesker » Thu Sep 26, 2013 3:11 am

Worked like a charm. I had squared it once but did not see to squser it twice. Thanks!


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