Chapter A.10, Problem 57AYU

To determine

To find: Solve the equation $\sqrt{15-2x}=x$ and get the value of $x$.

Answer to Problem 57AYU

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

Explanation of Solution

Given:

It is asked to find the solution for the given equation $\sqrt{15-2x}=x$.

Calculation:

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

The given equation contains a radical whose index is 2.

$\sqrt{15-2x}=x$

Raising power 2 on both the side and solve.

${\left(\sqrt{15-2x}\right)}^2={\left(x\right)}^2$

$15-2x=x^2$

$x^2+2x-15=0$

$\left(x+5\right)\left(x-3\right)=0$

$x=3$ or $x=-5$