Question

If
$5 \sqrt{3 } + 3 \sqrt{2} - 6 \sqrt{3} + 7 \sqrt{2} = a \sqrt{3} + b \sqrt{2}$
then find a and b

Answer 1

Hopeing you get this !
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Answer 2

Here is your answer

$5 \sqrt{3} + 3 \sqrt{2} - 6 \sqrt{3} + 7 \sqrt{2} \\ = 5 \sqrt{3} - 6 \sqrt{3} + 3 \sqrt{2} + 7 \sqrt{2} \\ = (5 - 6) \sqrt{3} + (3 + 7) \sqrt{2} \\ = - 1 \sqrt{3} + 10 \sqrt{2} \\ = a \sqrt{3} + b \sqrt{2}$
On Comparing
a = -1
b = 10

Hope it helps you