Question

if x= 1÷3-2root 2 and y = 1÷3+2 root.then find x+y+ xy

Answer 1

Hello mate!.....

$given..... \\ x = \frac{1}{3 - 2 \sqrt{2} } \\ y = \frac{1}{3 + 2 \sqrt{2} } \\ \\ x + y + xy = > \\ \\ 1)x + y = \frac{1}{3 - 2 \sqrt{2} } + \frac{1}{3 + 2 \sqrt{2} } \\ x + y= \frac{3 + 2 \sqrt{2} + 3 - 2 \sqrt{2} }{(3 - 2 \sqrt{2})(3 + 2 \sqrt{2}) } \\ x + y = \frac{6}{9 - 8} \\ x + y = 6.......eq1 \\ \\ xy = \frac{1}{3 - 2 \sqrt{2} } \times \frac{1}{3 + 2 \sqrt{2} } \\ xy = \frac{1}{(3 - 2 \sqrt{2})(3 + 2 \sqrt{2}) } \\ xy = \frac{1}{9 - 8} \\ xy = 1......eq2 \\ \\ from \: eqs \: 1and \: 2 \\ x + y + xy = 6 + 1 \\ x + y + xy = 7 \\ \\ hope \: it \: helps \: u \: dear....$