Question

find the value of a and b if 6-4√2/6+4√2=a+b√2.​

Answer 1

$\huge \bf \frac{6 - 4 \sqrt{2} }{6 + 4 \sqrt{2} } = a + b\sqrt{2} \\ \\ \\ \tt = > \frac{6 - 4 \sqrt{2}(6 - 4 \sqrt{2} ) }{6 + 4 \sqrt{2}(6 - 4 \sqrt{2} ) } = a + b\sqrt{2} \\ \\ \tt {= > \frac{ {(6)}^{2} + { (4 \sqrt{2} )}^{2} - 2(6)(4 \sqrt{2} )}{ {(6)}^{2} - {(4 \sqrt{2}) }^{2} } = a + b\sqrt{2} } \\ \\ \tt = > \frac{36 - 48 \sqrt{2} + 32}{36 - 32} = a + b \sqrt{2} \\ \\ \tt = > \frac{68 - 48 \sqrt{2} }{4} = a + b \sqrt{2} \\ \\ \tt = > \frac{68}{4} + \bigg( - \frac{48 \sqrt{2} }{4} \bigg) = a + b \sqrt{2}$

Hence,

$\boxed{ \sf a \: \: = {\frac{68}{4}} \: \: = \red{17}} \\ \\ \boxed{ \sf b \: \: = {\frac{ - 48}{4}} \: \: = \red{ - 12}}$