Question

if x^4+1/x^4=119 THEN FIND x^3-1/x^3

Answer 1

Hi,

Here's ur answer:-

x⁴+ 1/x⁴ = 119

=> (x²+1/x²)² - 2(x²)(1/x²) = 119

(x² and 1/x² are deduced)

=> (x²+1/x²)² = 119+2 = 121

=> x²+1/x² = 11

=> (x+1/x)²- 2(x)(1/x) = 11

(x and 1/x are deduced)

=> (x+1/x)²-2 = 11

=> (x+1/x)² = 11+2=13

=> x + 1/x = √13

We know that (a-b)³ = a³-b³-3a²b+3ab² = a³-b³-3ab(a-b)

=> a³-b³ = (a-b)³+3ab(a-b)

Using the above formula,

=> x³-1/x³ = (x-1/x)³+ 3(x)(1/x)(x-1/x)

Before doing that we have to find x - 1/x which is in this equation.

x²+1/x² = (x-1/x)²+2(x)(1/x)

(x and 1/x are deduced)

=> (x-1/x)²+2 = x²+1/x²

(putting the value of x²+1/x² from very top)

=> (x-1/x)² = 11-2 = 9

=> x-1/x = 3

Then let's come to the previous equation.

=> x³-1/x³ = (x-1/x)³+ 3(x)(1/x)(x-1/x)

(x and 1/x are deduced and value of x-1/x)

=> x³-1/x³ = 3³+ 3×3

=> x³-1/x³= 27+9 = 36

So, the final answer is 36.

HOPE IT HELPS (^_^)

Answer 2

Answer:

${a}^{3} - \frac{1}{ {a}^{3} } = 36$

I have taken x as a

hope it will help u..