Question

5+2√3÷7+4√3=a+b√3 what is a or b

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

Answer 2

$\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } =a + b \sqrt{3} \\ = \sqrt{3}^{5 + 2 - 7 + 4} = a + b \sqrt{3} \\ \sqrt{3} ^{11 - 7} = a + b \sqrt{3} \\ \sqrt{3} ^{4} = a + b \sqrt{3} \\ a + b = \frac{ { \sqrt{3} }^{4} }{ \sqrt{3} } \\ a + b = \sqrt{ {3} ^{3} } = 3 \sqrt{3}$