In each of these questions, two equations are given . You have to solve both the equations and give answer
I. ` sqrt( x + 4) = sqrt( 225) - sqrt( 121)`
II. ` y^(1) + 329 = 473`

Options

A. If ` x gt y `
B. If ` x ge y`
C. If ` x lt y `
D. If ` x le y `

Answer

To solve the given equations step by step, let's proceed as follows:

### Step 1: Solve the first equation
The first equation is:
\[ \sqrt{x + 4} = \sqrt{225} - \sqrt{121} \]

**Hint:** Calculate the values of \(\sqrt{225}\) and \(\sqrt{121}\).

Calculating the square roots:
\[ \sqrt{225} = 15 \quad \text{and} \quad \sqrt{121} = 11 \]

Now substitute these values back into the equation:
\[ \sqrt{x + 4} = 15 - 11 \]
\[ \sqrt{x + 4} = 4 \]

**Hint:** To eliminate the square root, square both sides of the equation.

Now square both sides:
\[ (\sqrt{x + 4})^2 = 4^2 \]
\[ x + 4 = 16 \]

**Hint:** Isolate \(x\) by subtracting 4 from both sides.

Now, subtract 4 from both sides:
\[ x = 16 - 4 \]
\[ x = 12 \]

### Step 2: Solve the second equation
The second equation is:
\[ y^1 + 329 = 473 \]

**Hint:** Isolate \(y\) by subtracting 329 from both sides.

Subtract 329 from both sides:
\[ y = 473 - 329 \]
\[ y = 144 \]

### Step 3: Compare the values of \(x\) and \(y\)
Now we have:
\[ x = 12 \quad \text{and} \quad y = 144 \]

**Hint:** Determine the relationship between \(x\) and \(y\).

To compare:
\[ x < y \quad \text{(since 12 is less than 144)} \]

### Final Answer
Thus, the relationship is:
\[ x < y \]