Question

Determine whether the given values of variable is a solution of the quadratic equation or not. $\frac{x}{x+2}=\frac{1}{2};x=2$ and $x=1$

Answer 1

The given quadratic equation is $\frac{x}{x+2}=\frac{1}{2}$.

Substitute $x=2$ in the equation $\frac{x}{x+2}=\frac{1}{2}$ as follows:

$\frac{x}{x+2}=\frac{1}{2}\Rightarrow \frac{2}{2+2}=\frac{1}{2}\Rightarrow \frac{2}{4}=\frac{1}{2}\Rightarrow \frac{1}{2}=\frac{1}{2}$

which is true.

Therefore, $x=2$ is the solution of the given quadratic equation.

Now, substitute $x=1$ in the equation $\frac{x}{x+2}=\frac{1}{2}$ as follows:

$\frac{x}{x+2}=\frac{1}{2}\Rightarrow \frac{1}{1+2}=\frac{1}{2}\Rightarrow \frac{1}{3}=\frac{1}{2}$

which is not true.

Therefore, $x=1$ is not the solution of the given quadratic equation.

Hence, $x=2$ is the solution but $x=1$ is not the solution of the quadratic equation $\frac{x}{x+2}=\frac{1}{2}$.