MCQ
If $\text{x}=\frac{2}{3+\sqrt7},$ then $(x-3)^2 =$
- A$1$
- B$3$
- C$6$
- ✓$7$
✓
Answer
Correct option: D.
$7$
$\text{x}=\frac{2}{3+\sqrt7}=\frac{2}{3+\sqrt7}\times\frac{3-\sqrt7}{3-\sqrt7}=\frac{2(3-\sqrt7)}{3-\sqrt7}\\ \ =\frac{6-2\sqrt7}{9-7}=\frac{6-2\sqrt7}{2}=3-2\sqrt7$
Now $(\text{x}-3)^2=(\not3-\sqrt7-\not3)^2=\big(-\sqrt7\big)^2=7$
Hence, correct option is $(d).$
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