Question

if a=9-4√5 then find the value of (a-1/a)^2

Answer 1

we can write (a-1)/a = 1 - 1/a...........................eq1

a = 9 - 4√5 given

1/a = 1/9 - 4√5

now rationalising above equation we get

1/a = 9 + 4√5

Now putting this value in eq1

1 - (9 + 4√5) = -(8 + 4√5)

we have to find out (a-1/a)²

So, (-(8 + 4√5))² = 64 + 80 + 64√5 = 144 + 64√5