Question

If 5x –3y = 3 and xy = 2, find the value of: 25x^2+ 9y^2.

Answer 1

Answer:

$(5x –3y) = 3 \\ squaring \: both \: sides \\ {(5x –3y)}^{2} = {3}^{2} \\ {(5x)}^{2} - 2(5x)(3y) + {(3y)}^{2} = 9 \\ {(5x)}^{2} + {(3y)}^{2} - 30xy = 9 \\ 25 {x}^{2} + 9 {y}^{2} - 30(2) = 9 \\ 25 {x}^{2} - 9 {y}^{2} = 9 + 60 \\ 25 {x}^{2} - 9 {y}^{2} = 69$