If x + y = 8 and xy = 3(3/4) , find the values of (i) x - y (ii) 3(x 2 + y 2 ) (iii) 5(x 2 + y 2 ) + 4(x - y).

(i) 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. ∴ (x - y) = . Substituting values we get, Hence, x - y = ±7. (ii) We know that, 3(x 2 + y 2 ) = 3[(x + y) 2 - 2xy]. Substituting values we get, Hence, 3(x 2 + y 2 ) = (iii) From parts (i) and (ii) we get, (x - y) = ±7 and x 2 + y 2 = . When (x - y) = 7, Substituting values we get, When (x - y) = -7, Substituting values we get, Hence, 5(x 2 + y 2 ) + 4(x - y) = .

JOIN NOW

Mathematics

If x + y = 8 and xy = 3(3/4) , find the values of (i) x - y (ii) 3(x2 + y2) (iii) 5(x2 + y2) + 4(x - y).

Expansions

59 Likes

Answered By

23 Likes

Mathematics

If x + y = 8 and xy = 3(3/4) , find the values of (i) x - y (ii) 3(x<sup>2</sup> + y<sup>2</sup>) (iii) 5(x<sup>2</sup> + y<sup>2</sup>) + 4(x - y).

Expansions

Related Questions

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

If a - b = 3 and ab = 4, find a³ - b³.

Mathematics

If x + y = 8 and xy = 3(3/4) , find the values of (i) x - y (ii) 3(x<sup>2</sup> + y<sup>2</sup>) (iii) 5(x<sup>2</sup> + y<sup>2</sup>) + 4(x - y).

Expansions

Related Questions

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

If a - b = 3 and ab = 4, find a3 - b3.

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

If a - b = 3 and ab = 4, find a³ - b³.