Question

If x=9+4√5,then find the value of √x-1/√x.​

Answer 1

given:x=9+4√5

=√(x-1)/√x

=√(9+4√5-1)/√(9+4√5)

=√(8+4√5)/√(9+4√5)

squaring the numerator and denominator,we get

=8+4√5/9+4√5

multiply by (9-4√5)in the numerator and denominator we get

=(8+4√5)(9-4√5)/(9+4√5)(9-4√5)

=72-32√5+36√5-80/(9)²-(4√5)²

=-8+4√5/81-80

=-8+4√5/1

=4(-2+√5)