Solve {l}{x=2}{y=3}{z=frac{sqrt{y}}{(x-y)^2}}

$$\left. \begin{array} { l } { x = 2 } \\ { y = 3 } \\ { z = \frac { \sqrt { y } } { ( x - y ) ^ { 2 } } } \end{array} \right.$$

Solve for x, y, z

$$x=2$$

$$y=3$$

$$z=\sqrt{3}\approx 1.732050808$$

Solution Steps

Consider the third equation. Insert the known values of variables into the equation.

$$z=\frac{\sqrt{3}}{\left(2-3\right)^{2}}$$

Subtract 3 from 2 to get -1.

$$z=\frac{\sqrt{3}}{\left(-1\right)^{2}}$$

Calculate -1 to the power of 2 and get 1.

$$z=\frac{\sqrt{3}}{1}$$

Anything divided by one gives itself.

$$z=\sqrt{3}$$

The system is now solved.

$$x=2 y=3 z=\sqrt{3}$$