12.2: Solve Blocks

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'solve' block

To use the solve block, first open the symbolic toolbar. We show how to solve the example 12.2.1 with this new technique.

Example 12.2.1

Solve 2 = x⁴+3x²−1.

Solution

In the worksheet, using ctrl + = for the bold symbolic equals sign and clicking on the word “solve” in the symbolic toolbar, the syntax is

2 = x⁴+3x²−1 solve, x →

Once you hit return, it will look like:

2 = x⁴+3x²−1 solve, x → \begin{pmatrix} -\sqrt{-\dfrac1{2}\sqrt{21}-\dfrac3{2}} \\ \sqrt{\frac{\sqrt{21}}{2}-\dfrac3{2}} \\ -\sqrt{-\dfrac1{2}\sqrt{21}-\dfrac3{2}} \\ \sqrt{\frac{\sqrt{21}}{2}-\dfrac3{2}} \nonumber\end{pmatrix}

If you type an equals sign on the end of the last line, it will become:

Note that two of these solutions are not real valued. Also, it is proper syntax to leave off the “, x” after the word solve as Mathcad will solve for the only variable present by default. That is,

2 = x⁴+3x²−1 solve, x →

will still give the same solution.

The solve block can be extended to equations with multiple variables as seen in the next example.

Example 12.1.2:

Solve 1 = x²y/x²+y² for each variable

Solution

Using the bold equals and the word “solve” from the symbolic toolbar, the syntax is:

\[1=\dfrac{x^{2}y}{x^{2}+y^{2}} solve, x→ \nonumber\]

Once you hit return, it will look like:

\[1=\dfrac{x^{2}y}{x^{2}+y^{2}} solve, x→ \nonumber\] \begin{pmatrix} -\dfrac{y}{\sqrt{y-1}} \\ \dfrac{y}{\sqrt{y-1}}\nonumber\end{pmatrix}

and

\[1=\dfrac{x^{2}y}{x^{2}+y^{2}} solve, x→ \nonumber\]

Once you hit return, it will look like:

\[1=\dfrac{x^{2}y}{x^{2}+y^{2}} solve, x→ \nonumber\] \begin{pmatrix} \dfrac{x(x+\sqrt{x^{2}-4})}{2} \\ \dfrac{x^{2}}{2}-\dfrac{x\sqrt{x^{2}-4}}{2}\nonumber\end{pmatrix}