Question

If x=2+√3 then find the value of x^2-1/x^2

Answer 1

x=2+√3, 1/x=2-√3 [ because If A^m =a+√b,A^-m=a-√b and vice versa]

x+1/x=2+√3+2-√3=4

x-1/x=2+√3-(2-√3)=2√3

now remember the identity ? a^2-b^2= (a+b) (a-b)

Similarly,x^2-1/x^2 =(x+1/x) (x-1/x)

=4×2√3

=8√3 ans