If `(sqrta+sqrtb)=17` and `(sqrta-sqrtb)=1`, then the value of `sqrtab` is :

Options

A. 72
B. 27
C. 35
D. none of these

Answer

To solve the equations \( \sqrt{a} + \sqrt{b} = 17 \) and \( \sqrt{a} - \sqrt{b} = 1 \), we can follow these steps:

### Step 1: Set Up the Equations
We have two equations:
1. \( x + y = 17 \) (where \( x = \sqrt{a} \) and \( y = \sqrt{b} \))
2. \( x - y = 1 \)

### Step 2: Solve for \( x \) and \( y \)
We can solve these equations simultaneously.

Add the two equations:
\[ (x + y) + (x - y) = 17 + 1 \]
This simplifies to:
\[ 2x = 18 \implies x = 9 \]

Now substitute \( x = 9 \) back into one of the original equations to find \( y \):
\[ 9 + y = 17 \implies y = 17 - 9 = 8 \]

### Step 3: Find \( \sqrt{a} \) and \( \sqrt{b} \)
Now we have:
\[ \sqrt{a} = x = 9 \quad \text{and} \quad \sqrt{b} = y = 8 \]

### Step 4: Calculate \( \sqrt{ab} \)
Now we can find \( \sqrt{ab} \):
\[ \sqrt{ab} = \sqrt{a} \cdot \sqrt{b} = 9 \cdot 8 = 72 \]

### Final Answer
Thus, the value of \( \sqrt{ab} \) is \( 72 \).

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