Question

If a and b are rational numbers, find the values of a and b in the following equality

5+2√3 ÷7+4 √3 = a + b √ 3

Answer 1

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