Question

if x^2+1/x=4,find 2x^3+2/x^3​

Answer 1

squaring on both sides we get, x^2+1/x^2+2=16 => x^2+1/x^2=14

(x+1/x)^3= x^3+1/x^3+3(x*1/x)*(x+1/x)

64=x^3+1/x^3+3(4)

x^3+1/x^3=64–12=52

hence 2*x^3+2/x^3 =52*2=104