Question

if 3x -4y=10 and xy =-1 find the value of 9 x ^2 + 16y^2

Answer 1

Hi
Nice question

Solution :-

Given :-

3x - 4y = 10
and
xy = -1

Using formula

(x - y)^2 = x^2 + y^2 - 2xy

Squaring 3x - 4y

${(3x - 4y)}^{2} = {(3x)}^{2} + {(4y)}^{2} - 2(3x)(4y) \\ \\ {(3x - 4y)}^{2} = 9 {x}^{2} + 16 {y}^{2} - 24xy \\ \\ {(10)}^{2} = 9 {x}^{2} + 16 {y}^{2} - 24( - 1) \\ \\ 100 = 9 {x}^{2} + 16 {y}^{2} + 24 \\ \\ 9 {x}^{2} + 16 {y}^{2} = 100 - 24 \\ \\ 9 {x}^{2} + 16 {y}^{2} = 76$

Hope this helps you.