Question

x_1/x=2then show that x^2_1/x^2= x^3_1/x^3=x^4_1/x^4​

Answer 1

Given:::X+1/X=2

now...

x²+1/x²=(x+1/x)²-2(x)(1/x)

=2²-2

=4-2

=2

x³+1/x³=(x+1/x){x²+1/x²-x.(1/x)}

=2(2-1)

=2

x⁴+1/x⁴=(x²+1/x²)²-2(x²)(1/x²)

=2²-2

=4-2

=2

therefore...x²+1/x²=x³+1/x³=x⁴+1/x⁴ [proved]