Question

Solve 1/2r^2-10= 3/2r2 using square roots. Select the solution(s).POSSIBLE SOLUTIONSA) r=(radical symbol here) -10B) r= -(radical symbol here) -10C) r= -(radical symbol here) 5D) r= (radical symbol here) 5E) no real solution

Answer 1

Answer:

There is no real solution

The solutions are imaginary, and they are:

$r=\sqrt[]{-10}$

and

$r=-\sqrt[]{-10}$

Explanation:

Given the equation:

$\frac{1}{2}r^2-10=\frac{3}{2}r^2$

To solve this, first subtract

$\frac{1}{2}r^2$

from both sides of the equation

$\begin{gathered} \frac{1}{2}r^2-10-\frac{1}{2}r^2=\frac{3}{2}r^2-\frac{1}{2}r^2 \\ \\ -10=r^2 \end{gathered}$

Next, take square root of both sides

$r=\pm\sqrt[]{-10}$

The solutions are:

$\begin{gathered} r=\sqrt[]{-10} \\ \\ \text{and} \\ \\ r=-\sqrt[]{-10} \end{gathered}$

There is no real solution, only imaginary.