Question : If $pq(p+q)=1$, then the value of $\frac{1}{p^{3}q^{3}}-p^{3}-q^{3}$ is equal to:
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Answer (1)
23rd Jan, 2024
Correct Answer: 3
Solution :
Given: $pq(p+q)=1$
⇒ $(p+q)=\frac{1}{pq}$
Cubing both sides,
⇒ $p^3+q^3+3pq(p+q)=\frac{1}{p^3q^3}$
Thus,
$\frac{1}{p^3q^3}–p^3–q^3= 3pq(p+q)$
Putting the value of $(p+q)=\frac{1}{pq}$
$= \frac{3}{pq}(pq)$
$=3$
$\therefore\frac{1}{p^3q^3}–p^3–q^3=3$
Hence, the correct answer is 3.
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