Question

if √3-√2 by√3+√2=a+b√6 find a and b

Answer 1

√3-√2 / √3 + √2 × √3 - √2 /√3 - √2. = (√3 -√2)^2 / √3^2 - √2^2. = 3+2-2√6 / 3 - 2. =5 - 2 √6 / 1. =5 - 2√6.
a = 5
b = -2

Answer 2

Hey friend,
Here is the answer you were looking for:
$\frac{( \sqrt{3)} - ( \sqrt{2}) }{( \sqrt{3)} + ( \sqrt{2}) } = a + b \sqrt{6} \\ = \frac{( \sqrt{3}) - ( \sqrt{2}) }{( \sqrt{3}) + ( \sqrt{2}) } \times \frac{( \sqrt{3}) - ( \sqrt{2} )}{( \sqrt{3}) - ( \sqrt{2}) } \\ = \frac{( \sqrt{3})^{2} + ( \sqrt{2}) ^{2} - 2 \times ( \sqrt{3} ) \times ( \sqrt{2} ) }{( \sqrt{3})^{2} - ( \sqrt{2})^{2} } \\ = \frac{3 + 2 - 2 \sqrt{6} }{3 - 2} \\ = 5 - 2 \sqrt{6}$
= 5 - 2√6 = a + b√6


= a = 5

= b = -2

Hope my answer would be helpful to you!!!

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@Mahak24

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