If a + b = 6 , a - b = 2 , then the value of `2 (a ^2 +b^2)` is :

Options

A. 20
B. 30
C. 40
D. 10

Answer

To solve the problem step by step, we start with the equations provided:

1. **Given Equations:**
- \( a + b = 6 \) (Equation 1)
- \( a - b = 2 \) (Equation 2)

2. **Add the two equations:**
\[ (a + b) + (a - b) = 6 + 2 \]
This simplifies to:
\[ 2a = 8 \]
Therefore, dividing both sides by 2:
\[ a = 4 \]

3. **Substitute the value of \( a \) back into Equation 1:**
\[ 4 + b = 6 \]
Solving for \( b \):
\[ b = 6 - 4 = 2 \]

4. **Now we have the values of \( a \) and \( b \):**
- \( a = 4 \)
- \( b = 2 \)

5. **Next, we need to find \( 2(a^2 + b^2) \):**
First, calculate \( a^2 \) and \( b^2 \):
\[ a^2 = 4^2 = 16 \]
\[ b^2 = 2^2 = 4 \]

6. **Now calculate \( a^2 + b^2 \):**
\[ a^2 + b^2 = 16 + 4 = 20 \]

7. **Finally, multiply by 2 to find \( 2(a^2 + b^2) \):**
\[ 2(a^2 + b^2) = 2 \times 20 = 40 \]

Thus, the value of \( 2(a^2 + b^2) \) is **40**.