Question

Si: x2 + y2 = 20, calcular: K = (x + y)2 + (x – y)2

Answer 1

Tienes que saber que:

${(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}$

${(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}$

Entonces:

$k = {(x + y)}^{2} + {(x - y)}^{2} \\ k = {x}^{2} + 2xy + {y}^{2} + {x}^{2} - 2xy + {y}^{2} \\ k =2 {x}^{2} + 2 {y}^{2} \\ k = 2( {x}^{2} + {y}^{2} ) \\ k = 2(20) \\ k = 40$