Question

If 2+√3\2-√3=a+b√3,find the value of a and b

Answer 1

Answer:

a = 7

b = 4

Solution:

We have:

(2+√3)/(2-√3) = a + b√3

Thus,

a + b√3 = (2+√3)/(2-√3) -------(1)

Now,

Rationalising the denominator of of the term in RHS of eq-(1) , we have ;

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

=> a + b√3 = (2+√3)²/ {2² - (√3)²}

=> a + b√3 = (2+√3)²/(4 - 3)

=> a + b√3 = (2+√3)²

=> a + b√3 = 2² + 2×2×√3 + (√3)²

=> a + b√3 = 4 + 4√3 + 3

=> a + b√3 = 7 + 4√3 -------(2)

Now,

Comparing the like terms in LHS and RHS of eq-(2) , we get ;

a = 7 and b = 4

Hence,

The required values of a and b are 7 and 4 respectively.