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

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by Max@Math Revolution » Thu Jan 24, 2019 5:10 am

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[Math Revolution GMAT math practice question]

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

A. 10
B. 12
C. 14
D. 16
E. 18
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If x+(1/x)=4, what is the value of x^2+(1/x^2)?

by fskilnik@GMATH » Thu Jan 24, 2019 5:15 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

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

A. 10
B. 12
C. 14
D. 16
E. 18
$$? = {x^2} + {1 \over {{x^2}}}$$
$$4 = x + {1 \over x}\,\,\,\,\mathop \Rightarrow \limits^{{\rm{squaring}}} \,\,\,\,16 = {x^2} + \left( {2 \cdot x \cdot {1 \over x}} \right) + {1 \over {{x^2}}}$$
$$? = {x^2} + {1 \over {{x^2}}} = 16 - 2 = 14$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by Max@Math Revolution » Sun Jan 27, 2019 5:08 pm
=>

( x + 1/x )^2 = x^2 + 2x(1/x) + (1/x)^2 = x^2 + (1/x)^2 + 2 = 4^2 = 16.
Thus, x^2 + (1/x)^2 = ( x + 1/x )^2 - 2 = 16 - 2 = 14.

Therefore, the answer is C.
Answer: C
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