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

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

$$\eqalign{ & pq\left( {p + q} \right) = 1 \cr & \Rightarrow p + q = \frac{1}{{pq}} \cr & \,\,\,\,\,\,\, \text{Cubing both side} \cr & \Rightarrow {p^3} + {q^3} +3 pq\left( {p + q} \right) = \frac{1}{{{p^3}{q^3}}} \cr & \,\,\,\,\,\,\, \text{Puting the value of } pq = \frac{1}{\left({p + q}\right)} \cr & \Rightarrow \frac{1}{{{p^3}{q^3}}} - {p^3} - {q^3} = \left( {\frac{{3}}{{p + q}}} \right)\left( {p + q} \right) \cr & \Rightarrow \frac{1}{{{p^3}{q^3}}} - {p^3} - {q^3} = 3 \cr} $$

Related Questions

Which of the following statements are true relating to payment of equal pay for equal work both for men and women?
1. ILO adopted equal remuneration Convention No. 100 in 1951.
2. India ratified ILO's Equal Remuneration Convention No. 100 in the year 1956.
3. Provisions relating to equal pay for equal work for both men and women are provided under Article 42 of the Indian Constitution.
4. The Equal Remuneration Ordinance was promulgated on 26th September, 1975.
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