Question

147) Find x^4 + 1 / x^4 if x - 1/x = 5Pls refer to pic for details

Answer 1

Given:

`x-(1)/(x)=5`

Asked: Find the value of:

`x^4+(1)/(x^4)`

Solution:

First, we need to find the value of x through the given.

`\begin{gathered} x-(1)/(x)=5 \\ (x-(1)/(x)=5)(x) \\ x^2-1=5x \\ x^2-5x-1=0 \end{gathered}`

We arrived with a quadratic equation so we will use this formula:

`\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{when }ax^2+bx+c=0 \end{gathered}`

Now, let's substitute the equation we have to the formula where a = 1, b = -5 and c = -1.