Question

If $\frac{5}{\sqrt{3}-\sqrt{2}}=a\sqrt{3}-b\sqrt{2}$, then the values of 'a' and 'b' are _________.

• A. $a=-5,b=-5$
• B. $a=-5,b=5$
• C. $a=5,b=-5$
• D. $a=5,b=5$

Answer 1

The correct option is C

$a=5,b=-5$

$\frac{5}{\sqrt{3}-\sqrt{2}}=a\sqrt{3}-b\sqrt{2}$

$\frac{5}{\sqrt{3}-\sqrt{2}}=a\sqrt{3}-b\sqrt{2}$

On rationalizing the denominator,

$\frac{5(\sqrt{3}+\sqrt{2})}{(\sqrt{3}{)}^2-(\sqrt{2}{)}^2}=a\sqrt{3}-b\sqrt{2}$

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

$5\sqrt{3}+5\sqrt{2}=a\sqrt{3}-b\sqrt{2}$

On comparing, we get $a=5,b=-5$.