Question

Please find the values of A and B​

Answer 1

ur answer is attached above.....

here,a=2 and b=5

stay safe ND have a nice day........

Answer 2

Question:-

Find the value of a and b, If

$\rm \: \frac{ \sqrt{2} + \sqrt{3} }{3 \sqrt{2 } - 2 \sqrt{3} } = a + b \sqrt{6}$

Solution:-

$\rm \: \frac{ \sqrt{2} + \sqrt{3} }{3 \sqrt{2 } - 2 \sqrt{3} } = a + b \sqrt{6}$

Take

$\rm \: \frac{ \sqrt{2} + \sqrt{3} }{3 \sqrt{2 } - 2 \sqrt{3} }$

Using rationalization method we get

$\rm \: \frac{ \sqrt{2} + \sqrt{3} }{3 \sqrt{2 } - 2 \sqrt{3} } \times \frac{3 \sqrt{2} + 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} }$

By using this identity , we get

$\to \rm \: ( \: a + b)(a - b) = ( {a}^{2} - {b}^{2} )$

$\rm \: (a + b)(c + d) = (ac + ad + bc + bd)$

Now we get ;

$\rm \: \frac{3 \sqrt{2 } \times \sqrt{2} + \sqrt{2} \times 2 \sqrt{3} + 3 \sqrt{2} \times \sqrt{3} + 2 \sqrt{3} \times \sqrt{3} }{(3 \sqrt{2}) {}^{2} - (2 \sqrt{3} ) {}^{2} }$

$\rm \: \frac{3 \times 2 + 2 \sqrt{6} + 3 \sqrt{6} + 2 \times 3 }{18 - 12}$

$\rm \: \frac{6 + 5 \sqrt{6} + 6}{6}$

$\rm \: \frac{12 + 5 \sqrt{6} }{6}$

Now value a and b are

$\rm \: \frac{12}{6} + \frac{5 \sqrt{6} }{6}$

Now

$\rm \: a = 2 \: \: \: and \: \: \: \: b = \frac{5}{6}$