Question

Find the value of A and B Root 3 + 1 divided by root 3 - 1 = A + root 3 × B

Answer 1

Answer:

A = 2 , B = 1

Solution:

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

We have ;

A + B√3 = (√3 + 1)/(√3 - 1)

Now,

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

A + B√3 = (√3 + 1)(√3 + 1) / (√3 - 1)(√3 + 1)

= (√3 + 1)² / [ (√3)² - 1² ]

= [ (√3)² + 2•√3•1 + 1² ] / (3 - 1)

= (3 + 2√3 + 1) / 2

= (4 + 2√3)/2

= 2(2 + √3)/2

= 2 + √3

Thus,

A + B√3 = 2 + √3

Now,

Comparing the like terms both the sides , we get ; A = 2 and B = 1

Hence,

A = 2 , B = 1