If a,b are rationals and `asqrt(2)+bsqrt(3)`
`=sqrt(98)+sqrt(108)-sqrt(48)-sqrt(72)` then the values of a,b are respectively

Options

A. a) `1,2`
B. b) `1,3`
C. c) `2,1`
D. d) `2,3`

Answer

To solve the equation \( a\sqrt{2} + b\sqrt{3} = \sqrt{98} + \sqrt{108} - \sqrt{48} - \sqrt{72} \), we will simplify the right-hand side step by step and compare coefficients to find the values of \( a \) and \( b \).

### Step 1: Simplify \( \sqrt{98} \)
\[ \sqrt{98} = \sqrt{2 \times 49} = \sqrt{2} \times \sqrt{49} = 7\sqrt{2} \]

**Hint:** Factor the number under the square root to find perfect squares.

### Step 2: Simplify \( \sqrt{108} \)
\[ \sqrt{108} = \sqrt{36 \times 3} = \sqrt{36} \times \sqrt{3} = 6\sqrt{3} \]

**Hint:** Look for the largest perfect square that divides the number.

### Step 3: Simplify \( \sqrt{48} \)
\[ \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3} \]

**Hint:** Again, factor to find perfect squares.

### Step 4: Simplify \( \sqrt{72} \)
\[ \sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2} \]

**Hint:** Use the same method of factoring for simplification.

### Step 5: Combine the simplified terms
Now substituting back into the equation:
\[ \sqrt{98} + \sqrt{108} - \sqrt{48} - \sqrt{72} = 7\sqrt{2} + 6\sqrt{3} - 4\sqrt{3} - 6\sqrt{2} \]

Combine like terms:
\[ = (7\sqrt{2} - 6\sqrt{2}) + (6\sqrt{3} - 4\sqrt{3}) = 1\sqrt{2} + 2\sqrt{3} \]

### Step 6: Set up the equation
Now we have:
\[ a\sqrt{2} + b\sqrt{3} = 1\sqrt{2} + 2\sqrt{3} \]

### Step 7: Compare coefficients
From the equation, we can compare coefficients:
- For \( \sqrt{2} \): \( a = 1 \)
- For \( \sqrt{3} \): \( b = 2 \)

### Final Answer
Thus, the values of \( a \) and \( b \) are:
\[ \boxed{(1, 2)} \]