Question

find a and b if 5+√3/3-2√3 = a + b√3​

Answer 1

Answer:

Solution:

Given (5 + 2√3)/(7 + 4√3) = a + b√3

Rationalizing the denominator on left-hand-side by multiplying the numerator and denominator with (7 - 4√3),

(5 + 2√3) (7 - 4√3)/(7 + 4√3) (7 - 4√3) = a + b√3

Multiply term by term the two expressions on numerator of L.H.S. and for the denominator apply the identity (m+n) (m-n) = m² - n² . We obtain,

(35 - 20√3 + 14√3 - 8.√3.√3)/[7² - (4√3)²] = a + b√3

Or, (35 - 6√3 - 8.3)/(49 - 48) = a + b√3

Or, (35 - 6√3 - 24)/1 = a + b√3

Or, 11 - 6√3 = a + b√3