If (x- \frac{1}{x} )^{2}=3, then the value of (x^{6}+ {1}/{x^{6}} )equals

SSC CGL Tier II 1 Dec 2016 Paper 1

Question : 70 of 100

Marks: +1, -0

(x- {1}/{x} )^{2}=3,

then the value of

(x^{6}+ {1}/{x^{6}} )

equals

Solution:

(3)

(x- {1}/{x} )^{2}=3

⇒ x^{2}+ {1}/{x^{2}}-2=3

⇒ x^{2}+ {1}/{x^{2}}=5

On cubing both sides,

(x^{2}+ {1}/{x^{2}} )^{3}=(5)^{3}

⇒ x^{6}+ {1}/{x^{6}}+3 (x^{2}+ {1}/{x^{2}} )=125

⇒x^{6}+ {1}/{x^{6}}+3 × 5=125

⇒ x^{6}+ {1}/{x^{6}}=125-15=110

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