Question

Find the values of a and b in each of the following:-

Help Me!...I literally gonna fail in Maths..

Give me a Brief explanation.. ​

Answer 1

Solution:-

${ \blue{ \boxed{\tt{ \underbrace{\underline{Solution:- }}}}}} \\ \\ { 1. \: \: \frac{3 + \sqrt{2} }{3 - \sqrt{2} } =a + b \sqrt{2} } \\ \\ { \longmapsto \tt{\frac{3 + \sqrt{2} }{3 - \sqrt{2} } =a + \sqrt{2b} }} \\ \\ {{ \longmapsto \tt{\frac{3 + \sqrt{2} }{3 - \sqrt{2} } - \sqrt{2b} \: \: =a }}} \\ \\ { \pink{ \longmapsto \tt{a = {\frac{3 + \sqrt{2} }{3 - \sqrt{2} } }}}} \\ \\ \\ {2. \: \: \frac{4 + 3 \sqrt{5} }{4 - 3 \sqrt{5} } = a + b \sqrt{5} } \\ \\ { \tt{ \longmapsto \: \: \frac{4 + 3 \sqrt{5} }{4 - 3 \sqrt{5} } = a + \sqrt{5b} }} \\ \\ { \tt{ \longmapsto \: \: \frac{4 + 3 \sqrt{5} }{4 - 3 \sqrt{5} } - \sqrt{5b} = a }} \\ \\ { \red{ \tt{ \longmapsto \: \: a= \frac{4 + 3 \sqrt{5} }{4 - 3 \sqrt{5} }}} } \\ \\ {\text{ \tt{now \: you \: to \: put \: value \: in \: \purple{b.}}}}$