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SSC CPO 2019 PYQ — Question 102

SSC CPO Tier I - 12th December 2019 - Shift 1 • Quantitative Aptitude • Q102

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If 8x/(2x2 + 7x - 2) = 1, x > 0 then, what is the value of x3 + (1/x3)?

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Correct answer: C

Explanation

The correct answer is Option 3 i.e.5(√17)/8

Application

Given that 8x/(2x2 + 7x - 2) = 1

8x = 2x2 + 7x - 2

2x2 - x - 2 = 0

Dividing by 2x

x - (1/2) - (1/x) = 0

x - (1/x) = 1/2

then, x + (1/x) = √{(x - 1/x)2 + (4x/x)}

= √(1/4 + 4)

= √17/2

Now, x3 + (1/x)3 = (x + 1/x)3 - 3x/x(x + 1/x)

(√17/2)3 - 3 × (√17/2)

= 5/8 × √17