Question

Find the values of a and 6
√3-1÷/3+1



= a +b√3
​

Answer 1

Answer :

a = 1 , 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 LHS , we have ;

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

=> (√3 - 1)²/[(√3)² - 1²] = a + b√3

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

=> (3 - 2√3 + 1)/2 = a + b√3

=> (2 - 2√3)/2 = a + b√3

=> 2(1 - √3)/2 = a + b√3

=> 1 - √3 = a + b√3

=> 1 + (-1)•√3 = a + b√3

Now ,

Comparing both the sides , we get ;

a = 1 and b = -1

Hence ,

a = 1 , b = -1