Question

Find a and b if 5 + square of 6 / 5- squAre root of 6 = a+bsquare root of 6

Answer 1

heya...!!!!

L.H.S

$\frac{5 + \sqrt{6} }{5 - \sqrt{6} } \\ \\ = > \frac{5 + \sqrt{6} }{5 - \sqrt{6} } \times \frac{5 + \sqrt{6} }{5 + \sqrt{6} } \\ \\ = > \frac{25 +6 + 10 \sqrt{6} }{25 - 6} \\ \\ = > \frac{31 + 10 \sqrt{6} }{19} \\ \\ = > \frac{31}{19} + \frac{10 \sqrt{6} }{19}$

on comparing with R.H.S

we get,

a = 31/19 ,b = 10√6/19

Answer 2

Hi ,

LHS = ( 5 + √6 )/(5 - √6 )

= [(5 + √6 ) (5 + √6 )]/[( 5-√6 ) ( 5 + √6 )]

= ( 5 + √6 )²/[ 5² - ( √6 )² ]

= ( 25 + 6 + 2 × 5 × √6 ) / ( 25 - 6 )

= ( 31 + 10√6 ) / 19

= 31/19 + ( 10/19) √6 ---( 1 )

RHS = a + b√6 -------( 2 )

compare ( 1 ) and ( 2 ) , we get

a = 31/19 ,

b = 10/19

I hope this helps you.

: )