x-2-5y-2-4xy-6y-9-0-find-xy-

Question Number 163746 by HongKing last updated on 10/Jan/22

x^{2} + {5 y}^{2} - 4 xy + 6 y + 9 = 0

find xy = ?

Answered by nurtani last updated on 10/Jan/22

x^{2} + 4 y^{2} - 4 x y + y^{2} + 6 y + 9 = 0 x 2

x^{2} + {(2 y)}^{2} - 4 x y + {(y + 3)}^{2} - 9 + 9 = 0

{(x - 2 y)}^{2} + 4 x y - 4 x y + {(y + 3)}^{2} = 0

{(x - 2 y)}^{2} + {(y + 3)}^{2} = 0

\Rightarrow x - 2 y = 0 \land y + 3 = 0

\Rightarrow x = 2 y \land y = - 3

∴ x y = 2 y (y)

= 2 y^{2}

= 2 {(- 3)}^{2}

= 2 (9) = 18

Answered by Rasheed.Sindhi last updated on 10/Jan/22

x^{2} - 4 x y + 4 y^{2} + y^{2} + 6 y + 9 = 0

{(x - 2 y)}^{2} + {(y + 3)}^{2} = 0

x - 2 y = 0 \land y + 3 = 0

y = - 3 \Rightarrow x = 2 y = 2 (- 3) = - 6

x y = (- 6) (- 3) = 18

Answered by kowalsky78 last updated on 10/Jan/22

x^{2} + 5 y^{2} - 4 x y + 6 y + 9 = {(x - 2 y)}^{2} + {(y + 3)}^{2} = 0

S o x = 2 y a n d y = - 3

x y = (- 6) \times (- 3) = 18

Commented by HongKing last updated on 10/Jan/22

very nice dear Sir thank you