If `a-b= 0.9` and ab= 0.36 find:
`a+b`

Answer

To solve the problem, we need to find the value of \( a + b \) given that \( a - b = 0.9 \) and \( ab = 0.36 \).

### Step-by-Step Solution:

1. **Start with the given equations**:
- \( a - b = 0.9 \) (Equation 1)
- \( ab = 0.36 \) (Equation 2)

2. **Use the identity for \( (a + b)^2 \)**:
We know that:
\[ (a + b)^2 = (a - b)^2 + 4ab \]

3. **Substitute the values from Equations 1 and 2**:
- First, calculate \( (a - b)^2 \):
\[ (a - b)^2 = (0.9)^2 = 0.81 \]
- Now substitute \( ab \) into the equation:
\[ 4ab = 4 \times 0.36 = 1.44 \]

4. **Combine the results**:
\[ (a + b)^2 = 0.81 + 1.44 \]
\[ (a + b)^2 = 2.25 \]

5. **Take the square root to find \( a + b \)**:
\[ a + b = \sqrt{2.25} = 1.5 \]

### Final Answer:
Thus, the value of \( a + b \) is \( 1.5 \).

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