Question

5 plus 2 root 3 divide by 7 + 4 root 3 equal to to a + b root 3​

Answer 1

(5+2√3)/(7+4√3) = a+b√3

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

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

35-20√3 + 14√3-24/49-48 = a+b√3

11-6√3 = a+b√3

On comparing both side we get-

a = 11

b = -6

Answer 2

$\color{red}\huge{\underline{\underline{\mathfrak{Answer}}}}$

LHS = (5+2√3)/(7+4√3)

= [(5+2√3)(7-4√3)]/[(7-4√3)(7+4√3)]

=[35-20√3+14√3-24]/[7²-(4√3)²]

=[11-6√3]/[49-48]

=11-6√3

therefore

11-6√3 = a+b√3

compare both sides

a= 11, b= -6