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SSC CHSL 2022 PYQ — Question 66

SSC CHSL - 26 May 2022 - Shift 3 • Quantitative Aptitude • Q66

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If (x + 1x\frac{1}{x}) = 115\frac{11}{5}, what is the value of (x3 + 1x3\frac{1}{x^3})?

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Correct answer: A

Explanation

The correct answer is option 1 i.e.  46125\frac{6}{125}

  According to formula,

x3+1x2=(x+1x)3−3(x+1x)⇒x3+1x2=(115)3−3(115)⇒x3+1x2=1331125−335⇒x3+1x2=506125⇒x3+1x2=46125\begin{aligned} & x^3+\frac{1}{x^2}=\left(x+\frac{1}{x}\right)^3-3\left(x+\frac{1}{x}\right) \\ & \Rightarrow x^3+\frac{1}{x^2}=\left(\frac{11}{5}\right)^3-3\left(\frac{11}{5}\right) \\ & \Rightarrow x^3+\frac{1}{x^2}=\frac{1331}{125}-\frac{33}{5} \\ & \Rightarrow x^3+\frac{1}{x^2}=\frac{506}{125} \\ & \Rightarrow x^3+\frac{1}{x^2}=4 \frac{6}{125}\end{aligned}