Question

Solve the equations with exponents.


x^2 + 5 = 20









m^3/3 - 2 = 22

Answer 1

Let's solve each equation step by step.

1. For the equation \( x^2 + 5 = 20 \):

\[
x^2 + 5 = 20
\]
Subtract 5 from both sides:
\[
x^2 = 20 - 5
\]
\[
x^2 = 15
\]
Now, take the square root of both sides:
\[
x = \pm \sqrt{15}
\]

2. For the equation \( \frac{m^3}{3} - 2 = 22 \):

\[
\frac{m^3}{3} - 2 = 22
\]
Add 2 to both sides:
\[
\frac{m^3}{3} = 22 + 2
\]
\[
\frac{m^3}{3} = 24
\]
Now, multiply both sides by 3:
\[
m^3 = 24 \times 3
\]
\[
m^3 = 72
\]
Now, take the cube root of both sides:
\[
m = \sqrt[3]{72}
\]

To simplify \( \sqrt[3]{72} \):
\[
72 = 2^3 \times 3^2
\]
Therefore,
\[
m = \sqrt[3]{2^3 \times 3^2} = 2 \sqrt[3]{9}
\]

Thus, the solutions to the equations are:
- For \( x^2 + 5 = 20 \): \( x = \pm \sqrt{15} \)
- For \( \frac{m^3}{3} - 2 = 22 \): \( m = 2 \sqrt[3]{9} \)