Question

If 5 + 2 root 3 / 7 + 4 root 3 = a + b root 3, find a and b.

Answer 1

I am not sure from my answer

Answer 2

Answer:

a = 11 and b = -6

Step-by-step explanation:

Here, the given expression is,

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

By rationalizing left side,

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

$\frac{35-20\sqrt{3}+14\sqrt{3}-24}{1}=a+b\sqrt{3}$

$\implies 11-6\sqrt{3}=a+b\sqrt{3}$

By comparing,

We get,

a = 11 and b= -6