Question

if 3x+2y=12,xy=6. find the value of 9x²+4y²

Answer 1

xy =6
x=6/y
3x+2y=12
3x6/y+2y=12
18/y+2y^2/y=12
18+2y^2=12y
2y^2 -12y+18=0
2y^2-6y-6y+18
2y(y-3)-6(y-3)
y=-6/2 y=-3
y=-3
xy=6
-3x=6
x=-2
9x^2+4y^2
9x4+4x9
36+36
72

Answer 2

$\Large{\underline{\underline{\bf{Solution:-}}}}$

$<strong>we</strong><strong> </strong>\:<strong> </strong><strong>have</strong>, \\ \\→ {(3x + 2y)}^{2} = {(3x)}^{2} + {(2y)}^{2} + 2 \times 3x \times 2y \\ \\→ {(3x + 2y)}^{2} = 9 {x}^{2} + 4 {y}^{2} + 12xy \\ \\→ {12}^{2} = 9 {x}^{2} + 4 {y}^{2} + 12 \times 6 \\ \\→ (putting \: \: 3x + 2y = 12 \: and \: xy = 6) \\ \\ →144 = 9 {x}^{2} + 4 {y}^{2} + 72 \\ \\ →144 - 72 = 9 {x}^{2} + 4 {y}^{2} \\ \\→ 9 {x}^{2} +4 {y}^{2} = 72$

$\Large{\underline{\underline{\bf{Thanks}}}}$