Question 60

If $$pq(p+q)=1$$, then the value of $$\frac{1}{p^3q^3}-p^3-q^3$$ is equal to

Solution

Given : $$pq(p+q)=1$$

=> $$p+q=\frac{1}{pq}$$ -----------(i)

Cubing both sides

=> $$(p+q)^3=(\frac{1}{pq})^3$$

=> $$p^3+q^3+3pq(p+q)=\frac{1}{p^3q^3}$$

=> $$p^3+q^3+3pq(\frac{1}{pq})=\frac{1}{p^3q^3}$$ [Using (i)]

=> $$\frac{1}{p^3q^3}-p^3-q^3=3$$

=> Ans - (C)

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