Question

If x= 1/3-2 root2 and Y= 1/3+2 root2 then find the value of x + y + xy.

Answer 1

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$x = \frac{1}{3 - 2 \sqrt{2} } \times \frac{3 + 2 \sqrt{2} }{3 + 2\sqrt{2} } \\ x = \frac{3 + 2 \sqrt{2} }{9 - 4 \times 2} = 3 + 2 \sqrt{2} \\ y = \frac{1}{3 + 2 \sqrt{2} } \times \frac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} } \\ y = \frac{3 - 2 \sqrt{2} }{9 - 4 \times 2} = 3 - 2 \sqrt{2} \\ x + y + xy \\ 3 + 2 \sqrt{2} + 3 - 2 \sqrt{2} + (3 + 2 \sqrt{2} )(3 - 2 \sqrt{2} ) \\ 6 +( 9 - 4 \times 2) \\ 6 + 1 = 7$

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Answer 2

I hope this will help ful for you