Question

if x is equals to 9 + 4 under root 5 find the value of under root x minus one upon under root under root x​

Answer 1

given,

x=9+4rt(5)

1/x=1/(9+4rt(5))

on rationalising with 9-4rt(5) we get

1/x=9-4rt(5)

now,

[rt(x)-1/(rt(x)]^2=x+1/x-2

=9+4rt(5)+9-4rt(5)-2

=16 i.e,

[rt(x)-1/rt(x)]^2=16

hence

rt(x)-1/rt(x)=(+/-)4