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If x^2+(1/x^2)=4, x^4+(1/x^4)=?

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If x^2+(1/x^2)=4, x^4+(1/x^4)=?

by Max@Math Revolution » Wed Apr 20, 2016 4:39 am
If x^2+(1/x^2)=4, x^4+(1/x^4)=?

A. 10
B. 11
C. 12
D. 14
E. 15


*A solution will be posted in two days.
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by Brent@GMATPrepNow » Wed Apr 20, 2016 6:18 am
Max@Math Revolution wrote:If x² + 1/x² = 4, then x� + 1/x� = ?

A. 10
B. 11
C. 12
D. 14
E. 15
IMPORTANT: I notice that if we SQUARE x², we get x�, and if we SQUARE 1/x², we get 1/x�, so let's see what happens if we take the equation x² + 1/x² = 4 and SQUARE both sides:

(x² + 1/x²)² = 4²
So, (x² + 1/x²)(x² + 1/x²) = 16
Expand to get: x� + 1 + 1 + 1/x� = 16
Simplify: x� + 1/x� = 14

Answer: D

Related Resource: Here's a free video on using the FOIL method to expand expressions: https://www.gmatprepnow.com/module/gmat ... /video/952

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by chetan.sharma » Wed Apr 20, 2016 9:00 am
Max@Math Revolution wrote:If x^2+(1/x^2)=4, x^4+(1/x^4)=?

A. 10
B. 11
C. 12
D. 14
E. 15


*A solution will be posted in two days.
Hi,
x^2+(1/x^2)=4,
Square both sides..
{x^2+(1/x^2)}^2=x^4+(1/x^4)+ x^4 *1/x^4= x^4+(1/x^4)+ 1..
so {x^2+(1/x^2)}^2 = (4)^2 = x^4+(1/x^4)+ 1..
so x^4+(1/x^4) = 16-2 =14
ans 15
D
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by Max@Math Revolution » Wed Apr 27, 2016 12:42 am
If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ?

A. 10
B. 12
C. 14
D. 16
E. 18


-> ==>x^4+(1/x^4)=(x^2)^2+(1/x^2)^2=(x^2+(1/x^2))^2-2x^2(1/x^2)=4^2-2=14

Thus, the answer is D.
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