Question

if x=7+4√3 and xy=1 then 1/x^2+1y^2​

Answer 1

Answer:

since x=7+4√3,so 1/x=1/7+4√3=7-4√3

and y=7-4√3,so 1/y=1/7-4√3=7+4√3

now, 1/x²+1/y²+2=(1/x+1/y)²

1/x²+1/y²+2=(7+4√3+7-4√3)²

1/x²+1/y²+2=(14)²

1/x²+1/y²=196-2

1/x²+1/y²= 194