Question

If x^4 +1/x^4 = 119 then the value of x^3 -1/x^3

Answer 1

Thanks for the question!

x^4 + 1/x^4 = 119

Adding 2 on both sides; 

x^4 + 1/x^4 +2 = 119 +2 

(x²+1/x²)²=121 

x²+1/x²=11

Adding -2 on both sides 

x²-2+1/x²=9

(x-1/x)²= 9 

x-1/x= ±3

Now, (x-1/x)³= x³-1/x³-3(x-1/x) 


Consider x-1/x= 3 .
3³ = x³-1/x³-3(3) 

27= x³-1/x³ - 9 

27+9=x³-1/x³ 

36 = x³-1/x³ 

consider x-1/x = -3 

-27 = x³-1/x³-3(-3) 

-27 = x³-1/x³+9 


-27-9 = x³-1/x³ 

x³-1/x³ = ±36 .