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If x+(1/x)=4, x2+(1/x2)=?

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by Max@Math Revolution » Sat Sep 24, 2016 9:41 pm
(ex 12) (equation) If x+(1/x)=4, x2+(1/x2)=?
A. 10 B. 12 C. 14 D. 16 E. 18
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by Brent@GMATPrepNow » Sun Sep 25, 2016 7:30 am
Max@Math Revolution wrote:(ex 12) (equation) If x + (1/x) = 4, x² + (1/x²) = ?
A. 10
B. 12
C. 14
D. 16
E. 18
Given: x + (1/x) = 4

NOTE: since there are squared terms in the expression we're trying to evaluate, we should consider squaring both sides.

Square both sides: [x + (1/x)]² = 4²
Rewrite as: [x + (1/x)][x + (1/x)] = 16
Use FOIL method to expand: x² + 1 + 1 + 1/x² = 16
Simplify: x² + 2 + 1/x² = 16
Subtract 2 from both sides: x² + 1/x² = 14

Answer: C

RELATED VIDEO
- FOIL method for expanding expressions: https://www.gmatprepnow.com/module/gmat ... /video/952

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by Max@Math Revolution » Tue Sep 27, 2016 8:08 am
==> x2+(1/x2)=(x+1/x)2-2x(1/x)=42-2=14 Thus the answer is C.
Answer: C
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