If `xy = 22 and x ^(2) + y ^(2) = 100,` then what will be the value of `(x + y)` ?

Options

A. 12
B. 144
C. 72
D. 6

Answer

To solve the problem, we are given two equations:

1. \( xy = 22 \)
2. \( x^2 + y^2 = 100 \)

We need to find the value of \( x + y \).

### Step 1: Use the identity for the square of a sum
We know that:
\[ (x + y)^2 = x^2 + y^2 + 2xy \]

### Step 2: Substitute the known values
From the given information, we can substitute \( x^2 + y^2 \) and \( xy \) into the equation:
\[ (x + y)^2 = 100 + 2 \cdot 22 \]

### Step 3: Calculate \( 2xy \)
Calculating \( 2 \cdot 22 \):
\[ 2xy = 44 \]

### Step 4: Add the values
Now substituting back into the equation:
\[ (x + y)^2 = 100 + 44 \]
\[ (x + y)^2 = 144 \]

### Step 5: Take the square root
To find \( x + y \), we take the square root of both sides:
\[ x + y = \sqrt{144} \]
\[ x + y = 12 \]

Thus, the value of \( x + y \) is \( 12 \).

---