If `a-b= 4 and a+b= 6`, find:
ab

Answer

To solve the problem, we need to find the value of \( ab \) given the equations:

1. \( a - b = 4 \)
2. \( a + b = 6 \)

### Step-by-step Solution:

**Step 1: Add the two equations.**

We start by adding the two equations to eliminate \( b \):

\[ (a - b) + (a + b) = 4 + 6 \]

This simplifies to:

\[ 2a = 10 \]

**Step 2: Solve for \( a \).**

Now, we divide both sides by 2 to find \( a \):

\[ a = \frac{10}{2} = 5 \]

**Step 3: Substitute \( a \) back into one of the original equations to find \( b \).**

We can use the first equation \( a - b = 4 \):

\[ 5 - b = 4 \]

Now, we solve for \( b \):

\[ b = 5 - 4 = 1 \]

**Step 4: Calculate \( ab \).**

Now that we have both \( a \) and \( b \), we can find \( ab \):

\[ ab = 5 \times 1 = 5 \]

### Final Answer:

Thus, the value of \( ab \) is \( 5 \).

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