Question

Quest
Find the value of a and b.
2+√3÷2-√3= a + b √3

vz = a buzz​

Answer 1

Answer:

a = 7

b = 4

Solution:

Given : (2 + √3)/(2 - √3) = a + b√3

To find : a = ? , b = ?

We have ;

a + b√3 = (2 + √3)/(2 - √3)

Now,

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

a + b√3 = (2 + √3)(2 + √3)/(2 - √3)(2 + √3)

= (2 + √3)²/{2² - (√3)²}

= {2² + (√3)² + 2•2•√3}/(4 - 3)

= (4 + 3 + 4√3)/1

= 7 + 4√3

Thus,

a + b√3 = 7 + 4√3

Now,

Comparing the like terms of RHS and LHS , we get : a = 7 , b = 4

Hence;

a = 7

b = 4