Question

I got this far and need to solve for x but don’t know how.

Answer 1

The question is:

`\begin{gathered} 5x^4-16x^2=16 \\ 5x^4-16x^2-16=0 \end{gathered}`

Factor as follows:

`\begin{gathered} 5x^4-16x^2-16=0 \\ 5x^4-20x^2+4x^2-16=0 \\ 5x^2(x^2-4)+4(x^2-4)=0 \\ (5x^2+4)(x^2-4)=0 \\ (5x^2+4)(x-2)(x+2)=0 \end{gathered}`

So the values of x are:

`\begin{gathered} x^2=-(4)/(5),x=2,-2 \\ x=\pm\frac{2}{\sqrt[]{5}}i,x=2,x=-2 \end{gathered}`

Hence there are two imaginary and two real roots for the equation.

The real roots are x=2 and x=-2.

Imaginary roots are:

`x=\frac{2}{\sqrt[]{5}}i,x=-\frac{2}{\sqrt[]{5}}i`