Question

Check your answer as simple as possible
(sqrt(1 + x ^ 2)) ^ 2 = 5 ^ 2 1 + x ^ 2 = 25 x ^ 2 = 25 - 1 x ^ 2 = 24 x = sqrt(2) * 40r - sqrt(24) x = 2sqrt(6) * or - 2sqrt(6)

Answer 1

Let's go through the calculations step by step for clarity.

1. Start with your equation:
\[
(\sqrt{1 + x^2})^2 = 5^2
\]

2. Simplify both sides:
\[
1 + x^2 = 25
\]

3. Subtract 1 from both sides:
\[
x^2 = 25 - 1
\]
\[
x^2 = 24
\]

4. Take the square root of both sides:
\[
x = \sqrt{24} \quad \text{or} \quad x = -\sqrt{24}
\]

5. Simplifying \(\sqrt{24}\):
\[
\sqrt{24} = \sqrt{4 \times 6} = 2\sqrt{6}
\]

6. Therefore, the solutions are:
\[
x = 2\sqrt{6} \quad \text{or} \quad x = -2\sqrt{6}
\]

Your final answers are correct:
\[
x = 2\sqrt{6} \quad \text{or} \quad x = -2\sqrt{6}
\]