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SSC CGL 2021 PYQ — Question 57

SSC CGL - 23 Aug 2021 - Shift 2 • Quantitative Aptitude • Q57

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If x + 1x\frac{1}{x} = 2√5 , then what is the value of (x4+1x2)x2+1\frac{\left( x^4 + \dfrac{1}{x^2} \right)}{x^2 + 1} ? 

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 17

Here it is given that, x + 1x\frac{1}{x} = 2√5

On cubing both sides we get,

= x3 + 1/x3 + 3(x + 1/x) = 40√5

= x3 + 1/x3 = 40√5 - 6√5 = 34√5.

we need to find the value of (x4+1x2)x2+1\frac{\left( x^4 + \dfrac{1}{x^2} \right)}{x^2 + 1} .

On dividing the equation by x in numerator and denominator we get,

= (x3 + 1/x3)/(x + 1/x)

= 34√5/2√5 = 17.