If x - y = 8 and xy = 5, find x 2 + y 2 .

We know that, (x - y) 2 = x 2 - 2xy + y 2 ⇒ x 2 + y 2 = (x - y) 2 + 2xy. Substituting values we get, ⇒ x 2 + y 2 = (8) 2 + 2 × 5 ⇒ x 2 + y 2 = 64 + 10 ⇒ x 2 + y 2 = 74. Hence, x 2 + y 2 = 74.

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Mathematics

If x - y = 8 and xy = 5, find x² + y².

Expansions

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Answer

We know that,

(x - y)² = x² - 2xy + y²

⇒ x² + y² = (x - y)² + 2xy.

Substituting values we get,

⇒ x² + y² = (8)² + 2 × 5
⇒ x² + y² = 64 + 10
⇒ x² + y² = 74.

Hence, x² + y² = 74.

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If x - y = 8 and xy = 5, find x² + y².

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