Question

if x =1/(3-2 root2) and y=1/(3+2 root 2) find xy2+x2y

Answer 1

$x = \frac{1}{3 - 2 \sqrt{2} } \\ x = \frac{1}{3 - 2 \sqrt{2} } \times \frac{3 + 2 \sqrt{2} }{3 + 2 \sqrt{2} } \\ x = 3 + 2 \sqrt{2} \\ \\ y = \frac{1}{3 + 2 \sqrt{2} } \\ y = 3 - 2 \sqrt{2} \\ \\ now \: \: \: x {y}^{2} + {x}^{2} y = xy(x + y) \\ = (3 + 2 \sqrt{2} )(3 - 2 \sqrt{2} )(3 + 2 \sqrt{2} + 3 - 2 \sqrt{2} ) \\ = (9 - 8)(6) \\ = 6$