Question

if a and bare rational no. find value of a and b in each of these. √3-1/√3+1=a+b√3

Answer 1

Hello Mate!

$\frac{ \sqrt{3} - 1}{ \sqrt{3} + 1} = a + b \sqrt{3} \\ \frac{ \sqrt{3} - 1}{ \sqrt{3} + 1} \times \frac{ \sqrt{3} - 1}{ \sqrt{3} - 1 } = a + b \sqrt{3} \\ \frac{3 + 1 - 2 \sqrt{ 3 } }{3 - 1} = a + b \sqrt{3} \\ 2 - \sqrt{3} = a + b \sqrt{3} \\ a = 2 \\ b = - 1$

Hope it helps☺!✌

Answer 2

Hi ,

LHS = ( √3 - 1 )/( √3 + 1 )

Rationalizing the denominator ,

= [ (√3 -1 )( √3 - 1 ) ] /[ ( √3 + 1 ) ( √3 - 1 ) ]

= ( √3 - 1 )² / [ ( √3 )² - 1² ]

= [ (√3 )² + 1² - 2 × √3 × 1 ] / ( 3 - 1 )

= ( 3 + 1 - 2√3 )/ 2

= ( 4 - 2√3 )/2

= 4/2 - 2√3/2

= 2 - √3

= 2 + ( -1 )√3 -----( 1 )

= a + b√3 -----( 2 ) [ given RHS

compare ( 1 ) & ( 2 ) ,

a = 2 ,

b = -1

I hope this helps you.

: )