Question

X+3y/x+y=3/2,then find value of x³+y³/x³-y³​

Answer 1

Answer:

14 / 13

Given

$\frac{x + 3y}{x + y} = \frac{3}{2} \\ \\ cross \: \: multiply\\ \\ 2(x + 3y) = 3(x + y) \\ \\ 2x + 6y = 3x +3 y \\ \\ x = 3y$

Put value of x in

$\frac{ {x}^{3} + {y}^{3} }{ {x}^{3} - {y}^{3} } \\ \\ = \frac{(3y) {}^{3} + {y}^{3} }{(3y) {}^{3} - {y}^{3} } \\ \\ = \frac{27 {y}^{3} + {y}^{3} }{27 y {}^{3} - {y}^{3} } \\ \\ = \frac{28 {y}^{3} }{26 {y}^{3} } \\ \\ = \frac{14}{13}$