Question

Find the value of x cube minus one by x cube if x minus one by x equal to 7

Answer 1

X - 1/x = X

On taking cube both side

(x - 1/x)^3 = x^3 +1/x^3 - 3(x^2)(1/x) + 3(x)(1/x^2)

(x - 1/x)^3 = x^3 + 1/x^3 - 3x + 3/x

On taking 3 common from RHS

(x - 1/x)^3 = x^3 + 1/x^3 - 3 (x - 1/x)

Now put value of x- 1/x = X

X^3 = x^3 + 1/x^3 - 3X

X^3 + 3X = x^3 + 1/x^3

Take X common from LHS

X (X^2 + 3) = x^3 + 1/x^3

Thanks

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Answer 2

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