Question

If 'a' and 'b' are rational numbers, find 'a' and 'b' given that $\frac{3}{\sqrt{3}-\sqrt{2}}=a\sqrt{3}-b\sqrt{2}$.

• A. $a=3,b=3$
• B. $a=3,b=-3$
• C. $a=1,b=-3$
• D. $a=3,b=1$

Answer 1

The correct option is B

$a=3,b=-3$

On solving the expression $\frac{3}{\sqrt{3}-\sqrt{2}}=a\sqrt{3}-b\sqrt{2}$,

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

$\Rightarrow$ $\frac{3(\sqrt{3}+\sqrt{2})}{3-2}=a\sqrt{3}-b\sqrt{2}$

$\Rightarrow$ $3\sqrt{3}+3\sqrt{2}=a\sqrt{3}-b\sqrt{2}$

$\therefore a=3,b=-3$