Question

if x^4+1/x^4=119 find x^3-1/x^3​

Answer 1

Answer:

x^4+1/x^4=119

=> (x^2)^2+1/(x^2)^2=119

=> (x^2+1/x^2)^2-2.x^2.1/x^2=119

=> (x^2+1/x^2)^2=119+2

=> (x^2+1/x^2)^2=121=(11)^2

=> x^2+1/x^2=11

=> (x-1/x)^2+2.x.1/x=11

=> (x-1/x)^2=11-2

=> (x-1/x)^2=9=(3)^2

=> x-1/x=3

x^3-1/x^3

=(x-1/x)^3+3.x.1/x(x-1/x)

=(3)^3+3.3

=27+9

=36