Question

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

Answer 1

The solution is given in the attachment....

hope it helps u....

Answer 2

Solution : 72

Given, 3x + 2y = 12 + 1

On squaring eqn → 1 on both the sides we get,

$\sf{ {(3x + 2y)}^{2} = {12}^{2}}$

$\sf{(3x)}^{2} + {(2y)}^{2} +2(3x)(2y) = 144$

$\sf since, {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab$

$\sf{9x}^{2} + {4y}^{2} + 12xy = 144$

given, xy = 6

$\sf {9x}^{2} + {4y}^{2} + 12(6) = 144$

$\sf {9x}^{2} + {4y}^{2}+ 72y = 144$

$\sf {9x}^{2} + {4y}^{2} = 144 - 72$

$\red{ \sf therefore , {9x}^{2} + {4y}^{2} = 72}$