Hello there,

Given that x^4 + 1/x^4 = 47, Now we have to find the value of x^3 + 1/x3.

So, we add and subtract 2 in the given equation

x^4 + 1/x4 +2 - 2 = 47, Now it can be written as

(x2)^2 + 1/(x2)^2 + 2. x^2.1/x^2 - 2 = 47

now, (x^2 + 1/x^2)^2 = 49

means, x^2 + 1/x^2 = 7, similarly adding and subtracting 2 we get that,

x + 1/x = 3,

And now the value of x^3 + 1/x3 is given as :

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

= 18

Hope it helps.