Question

x=(2+√5)1/2 +(2-√5)1/2 & y=(2+√5)1/2-(2-√5)then evaluate x²+y²

Answer 1

$x = \frac{1}{2} (2 + \sqrt{5} + 2 - \sqrt{5} ) \\ \\ x = \frac{1}{2} (4) \\ \\ x = 2$
similarly

$y = \frac{1}{2}(2 + \sqrt{5} - (2 - \sqrt{5} )) \\ \\ y = \frac{1}{2} (2 + \sqrt{5} - 2 + \sqrt{5} ) \\ \\ y = \frac{1}{2} (2 \sqrt{5} ) \\ \\ y = \sqrt{5}$

x+y=2+√5
Squaring both sides
x^2 +y^2+2xy = 4+5 + 4
√5

x^2 +y^2 =9+4√5 -2*2*√5

x^2 +y^2 = 9