If x^2 = 2x + 1, what is the value of x^3

Question

If x^2 = 2x + 1, what is the value of x^3 ？

A. 4x 
B. 5x + 2 
C. 5x - 1 
D. 3x + 2 
E. 3x - 2

KarishmaB · Accepted Answer

Given:  x^2 = 2x + 1

Multiply both sides by x to get
 
x^3 = 2x^2 + x

x^3 = 2(2x + 1) + x = 5x + 2

Answer (B)

gmatophobia · Answer

x^2 = 2x + 1

x^2 - 2x + 1 = 0

The roots of the equation can be found out by the formula  \frac{-b \pm\sqrt{b^2 - 4ac}}{2a}

Roots =  \frac{2 \pm\sqrt{4+4}}{2}

Roots =  \frac{2 \pm\sqrt{8}}{2}

=  \frac{2 \pm2\sqrt{2}}{2}  =  1\pm\sqrt{2}

Let's take only one root to calculate the value of  x^2  and  x^3

x = 1 + \sqrt{2}

x^3 = x^2 * x = (1+\sqrt{2})^2 * (1+\sqrt{2}) = 7 + \sqrt{2}

Using the option we can see that the value of  x^3  matches that of option B

Option B ⇒ 5x + 2

5(1+\sqrt{2}) + 2 = 7 + \sqrt{2}

Option B

radhikamehta · Answer

Hi,

How did you arrive at 
 5(1+\sqrt{2}) + 2 = 7 + \sqrt{2}

Isn't,  5(1 + \sqrt{2}) + 2 = 5 + 5\sqrt{2} + 2 = 7 + 5\sqrt{2}

Krunaal · Answer

That must be a typo, another way to approach this problem is:

x^3 = x^2 * x

Subs. value of  x^2

x^3 = (2x + 1)x

=  2x^2 + x

Subs. value of  x^2

=  2(2x + 1) + x

=  4x + 2 + x

=  5x + 2

If x^2 = 2x + 1, what is the value of x^3

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GMAT Problem Solving (PS) Questions

If x^2 = 2x + 1, what is the value of x^3

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