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