Given:
[tex]x-\frac{1}{x}=5[/tex]
Asked: Find the value of:
[tex]x^4+\frac{1}{x^4}[/tex]
Solution:
First, we need to find the value of x through the given.
[tex]\begin{gathered} x-\frac{1}{x}=5 \\ (x-\frac{1}{x}=5)(x) \\ x^2-1=5x \\ x^2-5x-1=0 \end{gathered}[/tex]
We arrived with a quadratic equation so we will use this formula:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{when }ax^2+bx+c=0 \end{gathered}[/tex]
Now, let's substitute the equation we have to the formula where a = 1, b = -5 and c = -1.
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