Chapter A.10, Problem 58AYU

To determine

To find: Solve the equation $\sqrt{12-x}=x$ and get the value of $x$.

Answer to Problem 58AYU

The solution for the given equation is $x=3$.

Explanation of Solution

Given:

It is asked to find the solution for the given equation $\sqrt{12-x}=x$.

Calculation:

Raise both the sides of the equation to same power and solve it.

The given equation contains a radical whose index is 2.

$\sqrt{12-x}=x$

Raising power 2 on both the side and solve.

${\left(\sqrt{12-x}\right)}^2={\left(x\right)}^2$

$12-x=x^2$

$x^2+x-12=0$

$\left(x+4\right)\left(x-3\right)=0$

$x=3$ or $x=-4$