Question

Find the value of a in:6÷3root2-2root3=3root2-a root3

Answer 1

$\frac6{3\sqrt2}-2\sqrt3=3\sqrt2-a\sqrt3\ \ \ \ \ \ /\times \sqrt2\\\frac6{3\sqrt2}\sqrt2-2\sqrt3\sqrt2=3\sqrt2\sqrt2-a\sqrt3\sqrt2\\2-2\sqrt6=6-a\sqrt6\\a\sqrt6=6-2+2\sqrt6\ \ \ \ \ \ /\div\sqrt6\\a=\frac4{\sqrt6}+2=\frac{4\sqrt6}6+2=2+\frac{2\sqrt6}3$