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29 Mar 2023, 03:45
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B
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Difficulty:
65%
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65% (01:58) correct
35%
(02:27)
wrong
based on 263
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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
A. 4x
B. 5x + 2
C. 5x - 1
D. 3x + 2
E. 3x - 2
29 Mar 2023, 23:31
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Bunuel
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)
General Discussion
29 Mar 2023, 22:53
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Bunuel
\(x^2 = 2x + 1\)
\(x^2 - 2x + 1 = 0\)
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
