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

Answer:- 1

Explanation:-

Solution:

\begin{aligned} p q (p + q) = 1 \\ \Rightarrow p + q = \frac{1}{p q} \\ \Rightarrow p^{3} + q^{3} + p q (p + q) = \frac{1}{p^{3} q^{3}} \\ \Rightarrow \frac{1}{p^{3} q^{3}} - p^{3} - q^{3} = (\frac{13}{p + q}) (p + q) \\ \Rightarrow \frac{1}{p^{3} q^{3}} - p^{3} - q^{3} = 3 \end{aligned}

$\eqalign{ & pq\left( {p + q} \right) = 1 \cr & \Rightarrow p + q = \frac{1}{{pq}} \cr & \Rightarrow {p^3} + {q^3} + pq\left( {p + q} \right) = \frac{1}{{{p^3}{q^3}}} \cr & \Rightarrow \frac{1}{{{p^3}{q^3}}} - {p^3} - {q^3} = \left( {\frac{{13}}{{p + q}}} \right)\left( {p + q} \right) \cr & \Rightarrow \frac{1}{{{p^3}{q^3}}} - {p^3} - {q^3} = 3 \cr}$

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p^{3}

${p^3}$ -

q^{3},

${q^3}{\text{,}}$ is equal to?", "text": "If pq(p + q) = 1, then the value of

\frac{1}{p^{3} q^{3}}

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

p^{3}

${p^3}$ -

q^{3},

${q^3}{\text{,}}$ is equal to?", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution: