Questions: x sqrt(y)-3=x-3 sqrt(y)

Transcript text: $x \sqrt{y}-3=x-3 \sqrt{y}$

Solution

Solution Steps

To solve the equation $x \sqrt{y} - 3 = x - 3 \sqrt{y}$, we can start by isolating terms involving $x$ and $\sqrt{y}$ on opposite sides of the equation. This will allow us to express one variable in terms of the other, or simplify the equation to find specific values for $x$ and $y$.

Step 1: Set Up the Equation

We start with the equation:

\[ x \sqrt{y} - 3 = x - 3 \sqrt{y} \]

Step 2: Rearrange the Equation

Rearrange the terms to isolate the terms involving $x$ and $\sqrt{y}$:

\[ x \sqrt{y} - x = 3 \sqrt{y} - 3 \]

Step 3: Factor and Simplify

Factor out common terms from both sides:

\[ x(\sqrt{y} - 1) = 3(\sqrt{y} - 1) \]

Step 4: Solve for $x$ and $\sqrt{y}$

Since $\sqrt{y} - 1$ is a common factor, we can divide both sides by $\sqrt{y} - 1$, assuming $\sqrt{y} \neq 1$:

\[ x = 3 \]