Question
If $\frac{5-\sqrt3}{2+\sqrt3}=\text{x}+\text{y}\sqrt3,$ then:
✓
Answer
- x = 13, y = -7
Solution:
$\frac{5-\sqrt3}{2+\sqrt3}$
$=\frac{5-\sqrt3}{2+\sqrt3}\times\frac{2-\sqrt3}{2-\sqrt3}$
$=\frac{\big(5-\sqrt3\big)\big(2-\sqrt3\big)}{(2)^2-\big(\sqrt3\big)^2}$
$=\frac{10-5\sqrt3-2\sqrt3+3}{4-3}$
$=\frac{13-7\sqrt3}{1}$
$=13-7\sqrt3$
⇒ x = 13 and y = -7
Hence, correct option is (a).
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