If x + y = 10 and xy = 21, find 2(x 2 + y 2 ).

We know that, (x + y) 2 = x 2 + 2xy + y 2 ⇒ x 2 + y 2 = (x + y) 2 - 2xy. ⇒ 2(x 2 + y 2 ) = 2[(x + y) 2 - 2xy] Substituting values we get, ⇒ 2(x 2 + y 2 ) = 2[(10) 2 - 2 × 21] ⇒ 2(x 2 + y 2 ) = 2(100 - 42) ⇒ 2(x 2 + y 2 ) = 2 × 58 ⇒ 2(x 2 + y 2 ) = 116. Hence, 2(x 2 + y 2 ) = 116.

Mathematics

If x + y = 10 and xy = 21, find 2(x² + y²).

Expansions

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Answer

We know that,

(x + y)² = x² + 2xy + y²

⇒ x² + y² = (x + y)² - 2xy.

⇒ 2(x² + y²) = 2[(x + y)² - 2xy]

Substituting values we get,

⇒ 2(x² + y²) = 2[(10)² - 2 × 21]

⇒ 2(x² + y²) = 2(100 - 42)

⇒ 2(x² + y²) = 2 × 58

⇒ 2(x² + y²) = 116.

Hence, 2(x² + y²) = 116.

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Mathematics

If x + y = 10 and xy = 21, find 2(x² + y²).

Expansions

Answer

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