Question

(3√2+2√3)/(5√2-4√3) = a-b√6 find the value of a and b

Answer 1

Hello Mate!

$\frac{3 \sqrt{2} + 2 \sqrt{3} }{5 \sqrt{2} - 4 \sqrt{3} } \times \frac{5 \sqrt{2} + 4 \sqrt{3} }{5 \sqrt{2} + 4 \sqrt{3} } \\ \frac{(3 \sqrt{2} + 2 \sqrt{3} )(5 \sqrt{2} + 4 \sqrt{3}) }{(25 \times 2) - (16 \times 3)} \\ \frac{30 + 12 \sqrt{6} + 10 \sqrt{6} + 24}{50 - 48} \\ \frac{54 + 22 \sqrt{6} }{28 } = 27 + 11 \sqrt{6} \\ 27 + 11 \sqrt{6} = a - b \sqrt{6} \\ 27 = a \: and \: b \: = - 11$

Hope it helps☺!