Question

if
X= ( 2+√ 5)^1/2 +(2-√ 5)^1/2
Y =(2+√ 5)^1/2 -(2-√5)^1/2
Then find X^2 +Y^2

Answer 1

X^2=(2+√5) +(2-√5) +2(2+√5) (2-√5)

= 4+2(4-5)

= 4-2

= 2

Y^2=(2+√5) +(2-√5) -2(2+√5) (2-√5)

= 4-2(4-5)

= 4+2

= 6

X^2+Y^2= 6+2

= 8