Question

Se (x - y)2 = 30 e x2 + y2 = 70, calcule (xy)2/4.

Answer 1

$\left \{ {{ (x-y)^{2}=30} \atop { x^{2} + y^{2} =70}} \right. \\ \\ \\ (x-y)^{2} =30 \\ \\ x^{2} -2xy+ y^{2}=30 \\ \\ x^{2} = 30+2xy-y^{2} } \\ \\ \\ x^{2} + y^{2} =70 \\ \\ 30+2xy- y^{2} + y^{2} =70 \\ \\ 2xy=70-30 \\ \\ xy= \frac{40}{2}=20 \\ \\ \\ \frac{(xy)^{2} }{4} = \frac{(20)^{2} }{4} = \frac{400}{4}=100$