$\displaystyle

\begin{array}{l}

solve\;in\;R \\

\\

x^4 - 2x^2 - 400x = 9999 \\

\end{array}

$

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- Jul 27th 2010, 05:26 AMfxs12equation 1
$\displaystyle

\begin{array}{l}

solve\;in\;R \\

\\

x^4 - 2x^2 - 400x = 9999 \\

\end{array}

$ - Jul 27th 2010, 05:32 AMProve It
Bring everything to one side

$\displaystyle x^4 - 2x^2 - 400x - 9999 = 0$.

Now work out the factors (positive and negative) of $\displaystyle 9999$.

Substitute each of these factors into the polynomial.

By the factor theorem, if any of these factors (call it $\displaystyle a$) makes the polynomial $\displaystyle = 0$, then $\displaystyle x - a$ is a factor. - Jul 27th 2010, 05:42 AMUnknown008
Solve in R? Do you mean for the real solutions?

Anyway, rearrange;

$\displaystyle x^4 - 2x^2 - 400x - 9999= 0$

Then, I'll use the factor theorem.

Let f(x) = x^4 - 2x^2 - 400x - 9999

By trial and error, find the values of x that are factors of 9999 that make f(x) = 0. Those are the factors of your equation.

Use long division or inspection to divide f(x) by their factors to get other factors, until you get a quadratic which is more easily factorised.

If it cannot be solved, then the values you got for f(x) = 0 are the only solutions.

EDIT: Woops, too late... I was making sure there were solutions =S