If pq(p + q) = 1, then the value of $$\frac{1}{{{p^3}{q^3}}}$$ - $${p^3}$$ - $${q^3}{\text{,}}$$ is equal to?
A. 1
B. 2
C. 3
D. 4
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & pq\left( {p + q} \right) = 1 \cr & \Rightarrow p + q = \frac{1}{{pq}} \cr & \,\,\,\,\,\,\, \text{Cubing both side} \cr & \Rightarrow {p^3} + {q^3} +3 pq\left( {p + q} \right) = \frac{1}{{{p^3}{q^3}}} \cr & \,\,\,\,\,\,\, \text{Puting the value of } pq = \frac{1}{\left({p + q}\right)} \cr & \Rightarrow \frac{1}{{{p^3}{q^3}}} - {p^3} - {q^3} = \left( {\frac{{3}}{{p + q}}} \right)\left( {p + q} \right) \cr & \Rightarrow \frac{1}{{{p^3}{q^3}}} - {p^3} - {q^3} = 3 \cr} $$Related Questions on Algebra
If $$p \times q = p + q + \frac{p}{q}{\text{,}}$$ then the value of 8 × 2 is?
A. 6
B. 10
C. 14
D. 16
A. $$1 + \frac{1}{{x + 4}}$$
B. x + 4
C. $$\frac{1}{x}$$
D. $$\frac{{x + 4}}{x}$$
A. $$\frac{{20}}{{27}}$$
B. $$\frac{{27}}{{20}}$$
C. $$\frac{6}{8}$$
D. $$\frac{8}{6}$$
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