Question

10 = 1 + \sqrt{81x}

Explanation:

🆕 New Concept Discovered: Solving Radical Equations
Isolate the root, then square both sides.

Step 1: Isolate the radical term

To solve for \(x\), we first need to get the square root term by itself on one side of the equation. We do this by subtracting \(1\) from both sides:

$$ 10 - 1 = \sqrt{81x} $$

$$ 9 = \sqrt{81x} $$

Step 2: Eliminate the radical

To undo the square root, we square both sides of the equation:

$$ (9)^2 = (\sqrt{81x})^2 $$

$$ 81 = 81x $$

Step 3: Solve for x

Divide both sides by \(81\) to find the value of \(x\):

$$ x = \frac{81}{81} $$

$$ x = 1 $$

Step 4: Verify the solution

Substitute \(x = 1\) back into the original equation to check if it is correct:

$$ 10 = 1 + \sqrt{81(1)} $$

$$ 10 = 1 + \sqrt{81} $$

$$ 10 = 1 + 9 $$

$$ 10 = 10 $$

The solution is correct.

Answer:

$$ x = 1 $$