[Math Revolution GMAT math practice question]
If x+(1/x)=4, what is the value of x^2+(1/x^2)?
A. 4
B. 10
C. 12
D. 14
E. 16
If x+(1/x)=4, what is the value of x^2+(1/x^2)?
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- Max@Math Revolution
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[x + (1/x)]² = 4²Max@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. 4
B. 10
C. 12
D. 14
E. 16
x² + 1/x² + 2(x)(1/x) = 16
x² + 1/x² + 2 = 16
x² + 1/x² = 14.
The correct answer is D.
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- fskilnik@GMATH
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FOCUS: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. 4
B. 10
C. 12
D. 14
E. 16
$$? = {x^2} + {1 \over {{x^2}}}$$
DATA:
$$x + {1 \over x} = 4\,\,\,\,\left( * \right)$$
FOCUS-DATA CONNECTION:
$$?\,\, = \,\,{x^2} + \underline 2 + {1 \over {{x^2}}} - \underline 2 \,\, = \,\,{\left( {x + {1 \over x}} \right)^2} - 2\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,\,{4^2} - 2 = 14$$
This solution follows the notations and rationale taught in the GMATH method.
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Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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- Max@Math Revolution
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=>
Since (a+b)^2=a^2+b^2+2ab, a^2+b^2=(a+b)^2-2ab, and
x^2 + 1/x^2 = ( x + 1/x )^2 - 2*x*(1/x) = 4^2 - 2 = 16 -2 = 14.
Therefore, the answer is D.
Answer: D
Since (a+b)^2=a^2+b^2+2ab, a^2+b^2=(a+b)^2-2ab, and
x^2 + 1/x^2 = ( x + 1/x )^2 - 2*x*(1/x) = 4^2 - 2 = 16 -2 = 14.
Therefore, the answer is D.
Answer: D
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We square both sides of the equation and obtain: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. 4
B. 10
C. 12
D. 14
E. 16
(x + (1/x))^2 = 4^2
x^2 + 2x(1/x) + (1/x)^2 = 16
x^2 + 2 + 1/x^2 = 16
x^2 + 1/x^2 = 14
Answer: D
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