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If x^2=x+1, then x^4=?

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by Max@Math Revolution » Fri Nov 30, 2018 12:45 am
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[Math Revolution GMAT math practice question]

If x^2=x+1, then x^4=?

A. 3x+2
B. 3x-2
C. 2x+3
D. 2x-3
E. 3x+4
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by GMATGuruNY » Fri Nov 30, 2018 5:38 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If x^2=x+1, then x^4=?

A. 3x+2
B. 3x-2
C. 2x+3
D. 2x-3
E. 3x+4
Squaring both sides, we get:
(x²)² + (x+1)²
x� = x² + 2x + 1

Substituting x²=x+1 into x� = x² + 2x + 1, we get:
x� = (x+1) + 2x + 1
x� = 3x + 2

The correct answer is A.
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by fskilnik@GMATH » Fri Nov 30, 2018 5:00 pm
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If x^2=x+1, then x^4=?

A. 3x+2
B. 3x-2
C. 2x+3
D. 2x-3
E. 3x+4
\[?\,\,\,:\,\,\,{x^4}\,\, = \,\,{\left( {{x^2}} \right)^2}\,\,\mathop = \limits^{\left( * \right)} \,\,{\left( {x + 1} \right)^2}\,\, = \,\,{x^2} + 2x + 1\,\,\mathop = \limits^{\left( * \right)} \,\,x + 1 + 2x + 1\]
\[?\,\, = \,\,3x + 2\]

This solution follows 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 Dec 02, 2018 5:42 pm
=>
x^4 = (x^2)^2 = (x+1)^2 = x^2 + 2x + 1 = (x + 1) + 2x + 1 = 3x + 2.
Therefore, the answer is A.
Answer: A
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