Question

Find the real solutions to the equation.
2,500=4x^4

Answer 1

To solve the equation \( 2500 = 4x^4 \), we start by isolating \( x^4 \):

\[
x^4 = \frac{2500}{4}
\]

Now, simplify the right side:

\[
x^4 = 625
\]

Next, to solve for \( x \), we take the fourth root of both sides:

\[
x = \pm \sqrt[4]{625}
\]

We know that:

\[
\sqrt[4]{625} = \sqrt{\sqrt{625}} = \sqrt{25} = 5
\]

Thus, the solutions for \( x \) are:

\[
x = 5 \quad \text{and} \quad x = -5
\]

Therefore, the real solutions to the equation \( 2500 = 4x^4 \) are:

\[
\boxed{5 \text{ and } -5}
\]