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x^2 + 4x + 1 = 0. What is the value of x^2 + 1/x^2?

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x^2 + 4x + 1 = 0. What is the value of x^2 + 1/x^2?

by Max@Math Revolution » Tue Apr 30, 2019 11:41 pm

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[GMAT math practice question]

x^2 + 4x + 1 = 0. What is the value of x^2 + 1/x^2?

A. 10
B. 12
C. 14
D. 16
E.18
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by GMATGuruNY » Wed May 01, 2019 2:29 am
Max@Math Revolution wrote:[GMAT math practice question]

x^2 + 4x + 1 = 0. What is the value of x^2 + 1/x^2?

A. 10
B. 12
C. 14
D. 16
E.18
x² + 4x + 1 = 0

Dividing both sides by x, we get:
(x² + 4x + 1)/x = 0/x
x + 4 + 1/x = 0
x + 1/x = -4

Squaring both sides, we get:
(x + 1/x)² = (-4)²
x² + 1/x² + 2(x)(1/x) = 16
x² + 1/x² + 2 = 16
x² + 1/x² = 14

The correct answer is C.
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by Max@Math Revolution » Thu May 02, 2019 11:01 pm
=>

x^2 + 4x + 1 = 0
=> x + 4 + 1/x = 0
=> x + 1/x = -4
So, (x + 1/x)2 = (-4)^2 and x^2 +2x(1/x) + 1/x^2 = 16.
Therefore,
x^2 +2 + 1/x^2 = 16
and x^2 + 1/x^2 = 14.

Therefore, the answer is C.
Answer: C
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