Question

if x is not equal to 0 and x+1/x=2 then show that x^2+1/x^2=x^3+1/x^3=x^4+1/x^4


please give me the answer

Answer 1

x+1/x=2
=>x+1=2x
=>x=1
so,LS= x²+1/x²=1+1/1=2
MS=x³+1/x³=1+1/1=2
RS=x⁴+1/x⁴=1+1/1=2
so LS=MS=RS [showed]