Question

If x+y =9 & x^2+y^2 ,xy=?

Answer 1

Given: x2−xy−10−2y2=0x2−xy−10−2y2=0;

Rearrange x2−y2−y2−xy−10=0x2−y2−y2−xy−10=0;

Apply a2−b2=(a−b)(a+b)a2−b2=(a−b)(a+b): (x−y)(x+y)−y2−xy−10=0(x−y)(x+y)−y2−xy−10=0 --> (x−y)(x+y)−y(y+x)−10=0(x−y)(x+y)−y(y+x)−10=0;

Factor out x+yx+y: (x+y)(x−y−y)−10=0(x+y)(x−y−y)−10=0;

Since given that x+y=2x+y=2, then we have that 2(x−2y)−10=02(x−2y)−10=0 --> x−2y=5