Question

x4 + 1/x4 = 47 find value of x3 + 1/x3

Answer 1

x4+1/x4+2-2=47
{(x2)2+2.x2.1/x2+(1/x2)2}47+2
(x2+1/x2)2=49
(x2+1/x2)2=72
x2+1/x2=7
x2+1/x2+2-2=7
x2+2.x2.1/x2+1/x2=7+2
(x+1/x)2=9
(x+1/x)2=3square
x+1/x=3
x3+1/x3
(x+1/x)3-3.x.1×(x+1/x)
(3)3-3(3)
27-9
18

Answer is 18...
...hope so will help...