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If x = 1

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If x = 1

by Max@Math Revolution » Thu Mar 12, 2020 12:17 am

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[GMAT math practice question]

If x = 1/2+ \(\sqrt{3}\) , what is x^2 - 4x?

A. -2
B. -1
C. 0
D. 1
E. 2
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Re: If x = 1

by Max@Math Revolution » Fri Mar 13, 2020 1:46 am
=>

We have
\(x=\frac{1}{2+\sqrt{3}}\)
\(x=\frac{2-\sqrt{3}}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}\) (multiplying by the conjugate)
\(x=\frac{2-\sqrt{3}}{4-3}\) (foiling the denominator)
\(x=2-\sqrt{3}\) (simplifying)
\(x-2=-\sqrt{3}\) (subtracting 2 from both sides)
\(\left(x-2\right)^2=\left(-\sqrt{3}\right)^2\) (squaring both sides)
\(x^2-4x+4=3\) (simplifying)
\(x^2-4x=-1\) (subtracting 4 from both sides)

Therefore, the answer is B.
Answer: B
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