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Bihar Police Constable Model Paper 1

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Question : 50 of 100

Marks: +1, -0

If

x-\frac{1}{x}

= 4, then the value of

x^3-\frac{1}{x^3}

is :

60
76
64
72

Solution:

Given:

x – 1/x = 4

Formula used:

(a-b)^3

=

a^3-b^3

– 3ab(a – b)

Calculation:

Our given expression is x – 1/x = 4

Taking cube on both the sides,

\left(x-\frac{1}{x}\right)^3

= 43

⇒

x^3-\frac{1}{x^3}

– 3x × 1/x(x – 1/x) = 64

⇒

x^3-\frac{1}{x^3}

– 3 × 4 = 64 ----(∵ x – 1/x = 4)

⇒

x^3-\frac{1}{x^3}

= 64 + 12

⇒

x^3-\frac{1}{x^3}

= 76

∴ The value of the given expression is 76

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