Question

4√3-6√5/7√5+3√3=a+b√15

Answer 1

$\bf HELLO\:\: DEAR,$



$\bf \frac{4\sqrt{3} - 6\sqrt{5}}{7\sqrt{5} + 3\sqrt{3}} = a + b\sqrt{15}$

$\bf \frac{4\sqrt{3} - 6\sqrt{5}}{7\sqrt{5} + 3\sqrt{3}} * \bf \frac{7\sqrt{5} - 3\sqrt{3}}{7\sqrt{5} - 3\sqrt{3}}$

$\bf \frac{4\sqrt{3}(7\sqrt{5} - 3\sqrt{3}) - 6\sqrt{5}(7\sqrt{5} - 3\sqrt{3})}{(7\sqrt{5})^{2} - (3\sqrt{3})^{2} }$

$\bf \frac{28\sqrt{15} - 36 - 210 + 18\sqrt{15}}{245 - 27}$

$\bf \frac{ - 246 + 46\sqrt{15} }{218}$

$\bf \frac{-246}{218} + \frac{46\sqrt{15}}{218}$

$\bf on \: \: comparing \: \: with \: \: R.H.S$

$\bf a = \frac{-123}{109} , b = \frac{23}{109}$

$\underline{\bf I \: \: HOPE \: \: \: \: ITS \: \: HELP \: \: YOU \: \: DEAR, \: \: THANKS}$