Question

if x is equal to root 3 + 1 by root 3 minus 1 Y is equal to root 3 minus 1 root 3 + 1 find the value of x square + 2 x y - x y square​

Answer 1

$x = \sqrt{3 + 1 } \div \sqrt{3 - 1} \\ y = \sqrt{ 3 - 1} \div \sqrt{3 + 1} \\ therefore \: x = 1 \div y \\ {x}^{2} + 2xy - {xy}^{2} = {x }^{2} + 2 \times 1 \div y \times y - {1 \div y}^{2} \times {y}^{2} \\ = {x}^{2} + 2 - 1 \\ = { \sqrt{3 + 1} } ^{2} \div { \sqrt{3 - 1 } }^{2} + 2 - 1 \\ = (3 + 1) \div (3 - 1) + 1 \\ = 4 \div 2 + 1 \\ = 2 + 1 = 3$