If a+ b =1 and a-b =7, find :
` ab `

Answer

To solve the equations \( a + b = 1 \) and \( a - b = 7 \) and find the value of \( ab \), we can follow these steps:

### Step 1: Write down the equations
We have two equations:
1. \( a + b = 1 \) (Equation 1)
2. \( a - b = 7 \) (Equation 2)

### Step 2: Add the two equations
To eliminate \( b \), we can add Equation 1 and Equation 2:
\[ (a + b) + (a - b) = 1 + 7 \]
This simplifies to:
\[ 2a = 8 \]

### Step 3: Solve for \( a \)
Now, divide both sides by 2 to find \( a \):
\[ a = \frac{8}{2} = 4 \]

### Step 4: Substitute \( a \) back into one of the equations
Now that we have \( a = 4 \), we can substitute this value into Equation 1 to find \( b \):
\[ 4 + b = 1 \]
Subtract 4 from both sides:
\[ b = 1 - 4 = -3 \]

### Step 5: Calculate \( ab \)
Now that we have both \( a \) and \( b \), we can find \( ab \):
\[ ab = a \cdot b = 4 \cdot (-3) = -12 \]

### Final Answer
Thus, the value of \( ab \) is \( -12 \).

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