Question

If x=1/3-2√2 and y=1/3+2√2 then find xy²+x²y

Answer 1

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