Question

find the value of a and b if a+b√7 = $\frac{3+2√7 }{3-2√7 }$

Answer 1

$a + b \sqrt{7} = \frac{3 + 2 \sqrt{7} }{3 - 2 \sqrt{7} }$



By Rationalization ,



$a + b \sqrt{7} = \frac{3 + 2 \sqrt{7} }{3 - 2 \sqrt{7} } \times \frac{3 + 2 \sqrt{7} }{3 + 2 \sqrt{7} } \\ \\ \\ \\ a + b \sqrt{7} = \frac{ {(3 + 2 \sqrt{7}) }^{2} }{ {(3)}^{2} - {(2 \sqrt{7} )}^{2} } \\ \\ \\ \\ a + b \sqrt{7} = \frac{9 + 28 + 4 \sqrt{7} }{9 -28 } \\ \\ \\ \\ a + b \sqrt{7} = \frac{37 + 4 \sqrt{7} }{ - 19} \\ \\ \\ \\ a + b \sqrt{7} = - \frac{37}{19} - \frac{4 \sqrt{7} }{19}$






Comparing values, we get

a = - 37 / 19

b = - 4 / 19