Question

If x+1/x = 2 then prove that x²+1/x² = x³+1/x³ = x⁴+1/x⁴​

Answer 1

Answer:

x+1/x=2

=> (x+1/x)^2=(2)^2

=> x^2+1/x^2+2.x.1/x=4

=> x^2+1/x^2+2=4

=> x^2+1/x^2=4-2

=> x^2+1/x^2=2

=> (x^2+1/x^2)^2=(2)^2

=> x^4+1/x^4+2.x^2.1/x^2=4

=> x^4+1/x^4+2=4

=> x^4+1/x^4=4-2

=> x^4+1/x^4=2

x+1/x=2

= > (x+1/x)^3=(2)^3

=> x^3+1/x^3+3.x.1/x(x+1/x)=8

=> x^3+1/x^3+3.2=8

=> x^3+1/x^3=8-6

=> x^3+1/x^3=2

so,

x^2+1/x^2=x^3+1/x^3=x^4+1/x^4=2