Question

If p+q=9 and p^2+q^2=51, find the value of pq.​

Answer 1

EXPLANATION.

⇒ p + q = 9. - - - - - (1).

⇒ p² + q² = 51. - - - - - (2).

As we know that,

We can write equation as,

⇒ p² + q² = 51.

⇒ (p + q)² - 2pq = 51.

Put the value of (p + q = 9) in the equation, we get.

⇒ (9)² - 2pq = 51.

⇒ 81 - 2pq = 51.

⇒ - 2pq = 51 - 81.

⇒ - 2pq = - 30.

⇒ 2pq = 30.

⇒ pq = 15.

Answer 2

Answer:

• The value of pq is 15.

Step-by-step explanation:

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Given,

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• $\tt p + q = 9$

• $\tt {p}^{2} + {q}^{2} = 51$

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To Find,

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• The value of pq.

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Solution,

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$\tt Identity \: \: 1 \\ \tt (a + b)^{2} = {a}^{2} + 2ab + {b}^{2}$

$:\implies\tt (p + q) ^{2} = {p}^{2} + {q}^{2} + 2pq \\ \\ :\implies\tt {(p + q)}^{2} - 2pq = {p}^{2} + {q}^{2} \\ \\ :\implies\tt {(9)}^{2} - 2pq = 51 \\ \\ :\implies\tt 81 - 2pq = 51 \\ \\ :\implies\tt - 2pq = 51 - 81 \\ \\ :\implies\tt - 2pq = - 30 \\ \\ :\implies \color{red} \boxed{\tt pq = 15}$

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Required Answer,

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• The value of pq is 15.