Question

5 plus root 3 by 7 plus2 root 3 is equal to a minus b root 3

Answer 1

5+√3/7+2√3 = a - b√3

LHS = 5+√3/7+2√3 x 7-2√3/7-2√3

= 5(7-2√3) + √3(7-2√3) / (7)² - (2√3)²

= 35-10√3+73-2√3+3 / 49 - 12

=38-5√3 / 37

RHS = a- b√3

substituting LHS into RHS, we get

a = 38/37

b√3 = 5√3 / 37

cancel √3 from both the sides

therefore,

a-b√3 = 38/37 - 5/37

here is your answer!