Question

5+2 root 3 / 7+4 root 3 =a-6root3

Answer 1

a = 11

Explanation:

`(5+2\sqrt3)/(7+4\sqrt3)\qquad\text{use}\ (a+b)(a-b)=a^2-b^2\\\\=(5+2\sqrt3)/(7+4\sqrt3)\cdot(7-4\sqrt3)/(7-4\sqrt3)=((5+2\sqrt3)(7-4\sqrt3))/(7^2-(4\sqrt3)^2)\qquad\text{use FOIL}\\\\=((5)(7)+(5)(-4\sqrt3)+(2\sqrt3)(7)+(2\sqrt3)(-4\sqrt3))/(49-4^2(\sqrt3)^2)\\\\=(35-20\sqrt3+14\sqrt3-8(3))/(49-(16)(3))=((35-24)+(-20\sqrt3+14\sqrt3))/(49-48)\\\\=(11-6\sqrt3)/(1)=11-6\sqrt3`