Question : If $2p + q = 19$ and $8p^3+q^3=361$, then find the value of $pq$.
Option 1: 56
Option 2: 59
Option 3: 58
Option 4: 57
Correct Answer: 57
Solution :
Given, $2\text{p} + \text{q} = 19$ and $\text{8p}^3 + \text{q}^3 = 361$
We have to find the value of pq
Consider $2\text{p} + \text{q} = 19$
Cubing both sides,
⇒ $\text{(2p+q)}^3 = \text{19}^3$
⇒ $(\text{2p})^3 + \text{q}^3 + \text{3(2p)(q)(2p+q)} = 6859$
⇒ $\text{8p}^3 + \text{q}^3 + \text{6pq(2p+q)} = 6859$
Putting the value $\text{8p}^3 + \text{q}^3 = 361$
⇒ $361 + \text{6pq}\times 19 = 6859$
⇒ $\text{114pq} = 6498$
⇒ $\text{pq} = \frac{6498}{114}$
⇒ $\text{pq}=57$
Hence, the correct answer is 57.
Related Questions
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Question : If $\frac{1}{p}+\frac{1}{q}=\frac{1}{p+q}$, the value of $\left (p^{3}-q^{3}\right )$ is:
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