SSC CGL 23 Aug 2021 Shift 1 Paper

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Question : 54 of 100

Marks: +1, -0

If

2 x^{2}-7 x+5=0

, then what is the value of

x^{3}+\;{125}/{8 x^{3}} ?

$12 \;{5}/{8}$
$16 \;{5}/{8}$
$18 \;{5}/{8}$
$10 \;{5}/{8}$

Solution:

Given,

2 x^{2}-7 x+5=0

Divided by

2 x

on both sides,

x+\;{5}/{2 x}=\;{7 x}/{2 x}

Cube on both sides,

(x+\;{5}/{2 x})^{3}=(\;{7}/{2})^{3}

⇒ \;\; x^{3}+\;{125}/{8 x^{3}}+3 × x × \;{5}/{2 x}(x+\;{5}/{2 x})

\;\; =\;{343}/{8}

⇒\;x^{3}+\;{125}/{8 x^{3}}=\;{343}/{8}-\;{15}/{2}(x+\;{5}/{2 x})

⇒\;x^{3}+\;{125}/{8 x^{3}}=\;{343}/{8}-\;{15}/{2} × \;{7}/{2}

\;\; =\;{343-105 × 2}/{8}

\;\; =\;{343-210}/{8}

(x^{3}+\;{125}/{8 x^{3}}) \;\; =\;{133}/{8}=16 \;{5}/{8}

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