Question

Soive the equation X-y=2 and x²+y²=52

Answer 1

Answer:

4 and 6

Step-by-step explanation:

$x - y = 2 \\ {(x - y)}^{2} = {2}^{2} \\ {x}^{2} + {y}^{2} - 2xy = 4 \\ 52 - 2xy = 4 \\ 2xy = 48 \\ xy = 24$

Substituting

$x - y= 2\\ y = x + 2$

Now

$xy = 24 \\ x(x + 2) = 24 \\ {x}^{2} + 2x - 24 = 0 \\ {x}^{2} + 6x - 4x - 24 = 0 \\ x(x - 6) - 4(x - 6) = 0 \\ (x - 4)(x - 6) = 0 \\ x = 4 \: or \: 6$

Hope it helps you.