Question

If =√3-1 / √3+1 = x+y√3, find the values of x and y.

Answer 1

Answer:

(√3 - 1)/(√3 + 1) × (√3 - 1)/(√3 - 1)

=> (√3 - 1)^2/(3 - 1)

=> (3 + 1 - 2√3)/2

=> (4 - 2√3)/2

=> 2(2 - √3)/2

=> 2 - √3

2 - √3 = x + y√3

=> x = 2

=> y = -1

______________

Answer 2

Given : √3 -1 / √3 + 1 = x + y√3.

 

To find : value of x and y.

 

We have , √3 -1 / √3 + 1

On Rationalising the denominator :  

= (√3 -1) (√3 - 1)

/ (√3 + 1)(√3 - 1)

= (√3 - 1)²/(√3² - 1²)

By Using Identity : (a - b)²  = a² + b² - 2ab & (a + b)(a – b) = a² - b²

= [√3² + 1² - 2 × √3 × 1] /( 3 - 1)

= [3 + 1 - 2√3]/2

= [4 -  2√3]/2

= 4/2 - 2√3/2

√3 -1 / √3 + 1 = 2 - √3  

∴ √3 -1 / √3 + 1  = x + y√3

= 2 - √3 = x + y√3

On equating rational and irrational parts :

x = 2 , y = - 1

Hence the value of  x is 2 and y is - 1.

HOPE THIS ANSWER WILL HELP YOU…..

 

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