Question

If k-1/k=3 then find the value of k³-1/k³

Answer 1

k - (1/k) = 3

Required= k^3 - (1/k)^3

We know that

(a-b)^3 = a^3 - b^3 -3ab(a-b)

(a-b)^3 + 3ab(a-b) = a^3 - b^3

here a = k , b= 1/k

(a-b)^3 + 3ab(a-b) = a^3 - b^3

(k -(1/k))^3 + 3×k×1/k (k - 1/k) = k^3 - 1/k^3

(k -(1/k))^3 + 3×1×(k - (1/k)) = k^3 - 1/k^3

substituting given value

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

27 + 9 = k^3 - 1/k^3

36 = k^3 - 1/k^3