If x + y = 6 and x - y = 4, find (i) x 2 + y 2 (ii) xy.

(i) We know that, (x + y) 2 = x 2 + y 2 + 2xy .....(i) (x - y) 2 = x 2 + y 2 - 2xy ....(ii) Adding eqn. (i) and (ii) we get, (x + y) 2 + (x - y) 2 = x 2 + x 2 + y 2 + y 2 + 2xy - 2xy = 2x 2 + 2y 2 . ⇒ 2x 2 + 2y 2 = (x + y) 2 + (x - y) 2 . ∴ x 2 + y 2 = Substituting values we get, Hence, x 2 + y 2 = 26. (ii) We know that, (x + y) 2 = x 2 + y 2 + 2xy .....(i) (x - y) 2 = x 2 + y 2 - 2xy ....(ii) Subtracting eqn. (ii) from (i) we get, (x + y) 2 - (x - y) 2 = x 2 - x 2 + y 2 - y 2 + 2xy - (-2xy) = 4xy. ⇒ (x + y) 2 - (x - y) 2 = 4xy. ∴ xy = Substituting values we get, Hence, xy = 5.

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Mathematics

If x + y = 6 and x - y = 4, find
(i) x² + y²
(ii) xy.

Expansions

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Mathematics

If x + y = 6 and x - y = 4, find
(i) x² + y²
(ii) xy.

Expansions

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Mathematics

If x + y = 6 and x - y = 4, find(i) x2 + y2(ii) xy.

Expansions

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