MCQ
If $\frac{2+\sqrt{3}}{2-\sqrt{3}}=\text{a}+\text{b}\sqrt{3},$ then,
- Aa = 7 and b = 4
- Ba = -7 and b = -4
- Ca = -7 and b = 4
- Da = 7 and b = -4
✓
Answer
- a = 7 and b = 4
Solution:
$\frac{2+\sqrt{3}}{2-\sqrt{3}}$
Multiplying numerator and denominator by $2\div\sqrt{3}$
So, $\frac{(2+\sqrt{3})^2}{(2-\sqrt{3})(2+\sqrt{3})}$
$=\frac{4+3+4\sqrt{3}}{4-3},$
$=7\div4\sqrt{3}$
Now equating $7\div4\sqrt{3}$ and $\text{a}\div\text{b}\sqrt{3}$
we get,
a = 7 and b = 4
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