Question

if x=2+√3, find the value of x³+⅓

Answer 1

Given that x=3+2√3 we need to find √x+1/√x. Therefore we have-

(√x+1/√x)^2= x+1/x +2 ...........using (a+b)^2=a^2+b^2+2ab

Substituting the value of x-

=(3+2√3)+1/(3+2√3)+2

Now, rationalize 1/x-

=(9+6√3-3+2√3+6)/3

=(12+8√3)/3

=4(3+2√3)/3

.

. . (√x+1/√x)=±(√(4(3+2√3)/3)

=±(2√(3+2√3)/3)

thanks