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SSC Selection Post 2020 PYQ — Question 72

SSC Selection Post - Matriculation Level 2020 - 9 Nov 2020 - Shift 1 • Quantitative Aptitude • Q72

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If x2 - 3\sqrt{3}x + 1 = 0, then (x3 + x-3) is equal to:

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 0.

x2−3x+1=0x^2 - \sqrt{3}x + 1 = 0

x+1x=3x + \frac{1}{x} = \sqrt{3}

(x+1x)3=x3+1x3+3(x+1x)\left(x + \frac{1}{x}\right)^3 = x^3 + \frac{1}{x^3} + 3\left(x + \frac{1}{x}\right)

(3)3=x3+1x3+33(\sqrt{3})^3 = x^3 + \frac{1}{x^3} + 3\sqrt{3}

33=x3+1x3+333\sqrt{3} = x^3 + \frac{1}{x^3} + 3\sqrt{3}

⇒x3+1x3=0\Rightarrow x^3 + \frac{1}{x^3} = 0