Question

X+1/x=4so prove that,xcube-1/xcube=30rude3

Answer 1

Answer:

x+1/x =4,

x^2+1/x^2+2.x.1/x=16,

x^2+1/x^2=14,

x^2+1/x^2-2*x*1/x=14-2,

(x-1/x)=√12,

x-1/x=2√3,

therefore,

x^3-1/x^3=(x-1/x)(x^2+X*1/X+1/x^2)

=(2√3)*(14+1)

=30√3

=rhs

hence,proved.