Question

if 3x-4y=10 and xy=1 find the value of 9xsquare +16ysquare

Answer 1

3x-4y = 10
squaring both side,
9x^2 +16y^2 - 24xy = 100
but xy = 1
so, 9x^2 - 16y^2 -24 = 100
9x^2 - 16y^2 = 124

Answer 2

$\bold{ 3x - 4y = 10} \\ \\ \\ \bold{ \underline{ \: square \: on \: both \: sides}} \\ \\ \\ \\ \bold{ {(3x - 4y)}^{2} = {10}^{2} } \\ \\ \\ \bold{ \: 9 {x}^{2} + 16 {y}^{2} - 2(3x \times 4y) = 100} \\ \\ \\ \bold{ \:9 {x}^{2} + 16 {y}^{2} - 24(xy) = 100} \\ \\ \\ \bold{ \: 9 {x}^{2} + 16 {y}^{2} - 24(1) = 100} \: \: \: \: \: \: \: \: \: \: \: \: \: \: (given \: that \: \: \: xy = 1) \\ \\ \\ \bold{ \: 9 {x}^{2} + 16 {y}^{2} = 100 + 24} \\ \\ \\ \bold{ \: 9 {x}^{2} + 16 {y}^{2} = 124}$