Question

Find the value of a and b if 5 + √6 / 5 - √6 = a + b √6

Answer 1

5 +√6/5-√6 =a +b √6
⇒5+(√6-5√6)/5 =a+b√6
⇒5 + (- 4√6 / 5 ) =a + b√6

Hence according to the fact that corresponding parts are equal
we have,
1..a =5
2..b = -4/5

Answer 2

Answer:

The value of $a= \frac {31}{19}$ and $b= \frac {10}{19}$  

To find:

The values of a and b from the given equation.  

Solution:

Given,

$\frac { 5 + \sqrt { 6 } } { 5 - \sqrt { 6 } } = a + b \sqrt { 6 }$

Rationalising the denominator, we get,

$\begin{array} { c } { \frac { 5 + \sqrt { 6 } } { 5 - \sqrt { 6 } } \times \frac { 5 + \sqrt { 6 } } { 5 + \sqrt { 6 } } = a + b \sqrt { 6 } } \\\\ { \frac { ( 5 + \sqrt { 6 } ) ( 5 + \sqrt { 6 } ) } { ( 5 - \sqrt { 6 } ) ( 5 + \sqrt { 6 } ) } = a + b \sqrt { 6 } } \\\\ { \frac { 25 + 5 \sqrt { 6 } + 5 \sqrt { 6 } + 6 } { 5 ^ { 2 } - \sqrt { 6 } ^ { 2 } } = a + b \sqrt { 6 } } \end{array}$

$\begin{array} { c } { \frac { 25 + 6 + 10 \sqrt { 6 } } { 5 ^ { 2 } - ( \sqrt { 6 } ) ^ { 2 } } = a + b \sqrt { 6 } } \\\\ { \frac { 31 + 10 \sqrt { 6 } } { 25 - 6 } = a + b \sqrt { 6 } } \\\\ { \frac { 31 + 10 \sqrt { 6 } } { 19 } = a + b \sqrt { 6 } } \\\\ { \frac { 31 } { 19 } + \frac { 10 } { 19 } \sqrt { 6 } = a + b \sqrt { 6 } } \end{array}$

$\therefore a = \frac { 31 } { 19 } , b = \frac { 10 } { 19 }$

Thus the value of $a = \frac { 31 } { 19 } , b = \frac { 10 } { 19 }$