Question

If $\frac{3+\sqrt{5}}{2\sqrt{5}+3}=a+b\sqrt{5}$, then the values of irrational numbers $a$ and $b$ are

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$\frac{3+\sqrt{5}}{2\sqrt{5}+3}=\frac{(3+\sqrt{5})(2\sqrt{5}-3)}{(2\sqrt{5}+3)(2\sqrt{5}-3)}=\frac{1+3\sqrt{5}}{20-9}=\frac{1}{11}+\frac{3}{11}\sqrt{5}\text{Hence, a}=\frac{1}{11}\text{and b}=\frac{3}{11}$