This task is not quite so simple. There are in fact many methods for solving rational equations, and about a hundred of these methods are used in our program. Try, for example to solve the following equations:

x^{4}=(x+1)(5x^{2}-6x-6)

(1+x+x^{2})^{4}=(1+x^{2}+x^{4})^{2}

(x^{2}+1)^{2}(x+1)=0.8

UMS solves rational, irrational, logarithmic, exponential and trigonometric equations.

**{** button and enter each of the equations on a separate line. To add the next equation, press the Enter button.

The UMS program considers this expression to already be in the simplest possible form. We recommend you select “Expand” in the “Mathematical Subject” menu.

The argument of the entered function must be enclosed in parentheses. For example f(x) = x^{2} – x^{3} or y(x) = x^{2} – x^{3}, or the argument can be omitted, for example y = x^{2} – x^{3}. In this case UMS would consider the expression as a function.

We recommend you select “Complete factoring” in the “Mathematical Subject” menu.

You need to use the quadratic function y = x^{2} + px + q: The graph of this function is a parabola with branches pointing up.

The Vertex of the parabola has an x-axis value of x = – p/2. In your example p = – 6a, x= – p/2 = 3a. In order for both roots of the quadratic function to be greater than some number c, it is necessary and sufficient for the system of three inequalities to be true:

In your example this system will look like this:

Or

This system of inequalities can be solved using UMS.

The equation was not written correctly. In your equation log(x) is raised to the square and to the fourth degree. If we write this equation in the form: log(x) + log(x^{2}) + log(x^{4}) = 7, then argument x is raised to the square and to the fourth degree. Now UMS can solve this simple equation.

In order to find the value F(c) of a function F=f(x) for the given value of variable x=c enter the following system and solve it with UMS.

In your example this system will look like this:

UMS solves this system and receives:that is P(45) = -599

You forgot to enter the degree sign. You must enter

Now UMS solves this problem and gives the right answer -1/2.

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