Question

find the value if a, b are rational and a√2+b√3=√98+√108-√48-√72​

Answer 1

$a \sqrt{2} + b \sqrt{3} = \sqrt{98} + \sqrt{108} - \sqrt{48} - \sqrt{72} \\ a \sqrt{2} + b \sqrt{3} = \sqrt{2 \times 7 \times 7} + \sqrt{2 \times 2 \times 3 \times 3 \times 3} - \sqrt{2 \times 2 \times 2 \times 2 \times 3} - \sqrt{2 \times 2 \times 2 \times 3 \times 3} \\ a \sqrt{2} + b \sqrt{3} = 7 \sqrt{2 } + 6 \sqrt{3} - 4 \sqrt{3} - 6 \sqrt{2} \\ a \sqrt{2} + b \sqrt{3} = \sqrt{2} + 2 \sqrt{3}$

Therefore, a= 1 and b= 2