Question

If x=
$\frac{ \sqrt{5 } + 1}{ \sqrt{5} - 1 }$
and y=
$\frac{ \sqrt{5} - 1}{ \sqrt{5} + 1 }$
find the value of
${x}^{2} + {y}^{2}$

Answer 1

X=(√5+1)/(√5-1)
Y=(√5-1)/(√5+1)

X^2 + Y^2 = {(√5+1)/(√5-1)} ^2 + {(√5-1)/(√5+1)}^2
= (5+1)/(5-1) +(5-1)/(5+1)
= (6)/(4) + (4)/(6)
= (3)/(2) + (2)/(3)
= (9+4)/6
= 13/6

X^2 + Y^2 = 13/6

This is your answer.....