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If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ?

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Joined: 24 May 2014
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Location: Brazil
If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ?  [#permalink]

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26 Jul 2014, 09:59
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68% (01:17) correct 32% (01:51) wrong based on 234 sessions

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If $$x^2 + \frac{1}{x^2} = 4$$, what is the value of $$x^4 + \frac{1}{x^4}$$ ?

A. 10
B. 12
C. 14
D. 16
E. 18
Math Expert
Joined: 02 Sep 2009
Posts: 58434
Re: If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ?  [#permalink]

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26 Jul 2014, 10:09
4
Reni wrote:
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

Square $$x^2 + \frac{1}{x^2} =4$$:

$$x^4+2*x^2*\frac{1}{x^2}+\frac{1}{x^4}=16$$;

$$x^4+2+\frac{1}{x^4}=16$$;

$$x^4+\frac{1}{x^4}=14$$.

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Re: If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ?  [#permalink]

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17 Mar 2016, 21:44
1
Squaring on both sides:$$(x^2 + \frac{1}{x^2})^2 = 16$$
$$x^4 + \frac{1}{x^4} + 2 = 16$$
$$x^4 + \frac{1}{x^4} = 14$$

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Re: If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ?  [#permalink]

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21 Mar 2016, 04:26
If x^2+(1/x^2)=4, x^4+(1/x^4)=?

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

-> 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.
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Re: If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ?  [#permalink]

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20 Apr 2016, 07:19
1
1
Reni wrote:
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

IMPORTANT: I notice that if we SQUARE x², we get x⁴, and if we SQUARE 1/x², we get 1/x⁴, 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: x⁴ + 1 + 1 + 1/x⁴ = 16
Simplify: x⁴ + 1/x⁴ = 14

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
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Re: If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ?  [#permalink]

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13 Sep 2019, 01:50
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Re: If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ?   [#permalink] 13 Sep 2019, 01:50
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