If x + y = 7 and x² + y² = 25, then find the value of √(xy).

Given, x + y = 7 x2 + y2 = 25 By using the identity, (x + y)2 = x2 + y2 + 2xy ⇒ (7)2 = 25 + 2xy ⇒ 49 = 25 + 2xy ⇒ 49 - 25 = 2xy ⇒ 2xy = 24 ⇒ xy = ⇒ xy = 12 ⇒ ⇒ ⇒ . Hence, .

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Mathematics

If x + y = 7 and x² + y² = 25, then find the value of $\sqrt{xy}$ .

Factorisation

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Answer

Given,

x + y = 7

x² + y² = 25

By using the identity,

(x + y)² = x² + y² + 2xy

⇒ (7)² = 25 + 2xy

⇒ 49 = 25 + 2xy

⇒ 49 - 25 = 2xy

⇒ 2xy = 24

⇒ xy = $\dfrac{24}{2}$

⇒ xy = 12

⇒ $\sqrt{xy} = \sqrt{12}$

⇒ $\sqrt{xy} = \sqrt{4 × 3}$

⇒ $\sqrt{xy} = 2\sqrt{3}$ .

Hence, $\sqrt{xy} = 2\sqrt{3}$ .

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If x + y = 7 and x² + y² = 25, then find the value of $\sqrt{xy}$ .

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