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

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

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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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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
x⁴ = x² + 2x + 1

Substituting x²=x+1 into x⁴ = x² + 2x + 1, we get:
x⁴ = (x+1) + 2x + 1
x⁴ = 3x + 2

The correct answer is A.

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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.

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English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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=>
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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The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Only $149 for 3 month Online Course
Free Resources-30 day online access & Diagnostic Test
Unlimited Access to over 120 free video lessons-try it yourself
Email to : info@mathrevolution.com

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