Question

5 + 2 root 3 upon 7 + 4 root 5 find a+b√3​

Answer 1

Question:- (5+2√3)/(7+4√5) = a + b√3; Find a and b

Answer: a = 11 and  b = -6

Step-by-step explanation:

We have,

$\frac{5+2\sqrt{3}}{7+4\sqrt{3}}=a+b\sqrt{3}\\\;\\\frac{(5+2\sqrt{3})(7-4\sqrt{3})}{(7+4\sqrt{3})(7-4\sqrt{3})}=a+b\sqrt{3}\\\;\\\frac{7\times5+5\times(-4\sqrt{3})+7\times2\sqrt{3}+2\sqrt{3}\times(-4\sqrt{3})}{(7^2-(4\sqrt{3})^2)}=a+b\sqrt{3}\\\;\\\frac{35-20\sqrt{3}+14\sqrt{3}-24}{49-48}=a+b\sqrt{3}\\\;\\11-6\sqrt{3}=a+b\sqrt{3}\\\;\\\text{On comparing both sides}\\\;\\\textbf{a\;=\;11\;\;and\;\;b\;=\;-6}$