Question

Find the values of a and b
13 + 1
10.
3-1
= a + bv3​

Answer 1

Answer :

a = 2 , b = 1

Solution :

• Given : (√3 + 1)/(√3 - 1) = a + b√3
• To find : a , b = ?

We have ,

(√3 + 1)/(√3 - 1) = a + b√3

Now ,

Rationalising the denominator of the term in RHS , we get ;

=> (√3 + 1)(√3 + 1)/(√3 - 1)(√3 + 1) = a + b√3

=> (√3 + 1)²/ [(√3)² - 1²] = a + b√3

=> [(√3)² + 1² + 2•√3•1] / [3 - 1] = a + b√3

=> (3 + 1 + 2√3)/2 = a + b√3

=> (4 + 2√3)/2 = a + b√3

=> 2(2 + √3)/2 = a + b√3

=> 2 + √3 = a + b√3

Now ,

Comparing both the sides , we get

a = 2

b = 1

Hence ,

a = 2 , b = 1