AP EAMCET · Maths · Quadratic Equation
If \(x=\sqrt{\frac{2+\sqrt{3}}{2-\sqrt{3}}}\), then \(x^2(x-4)^2\) is equal to :
- A 7
- B 4
- C 2
- D 1
Answer & Solution
Correct Answer
(D) 1
Step-by-step Solution
Detailed explanation
\(\because \quad x=\sqrt{\frac{2+\sqrt{3}}{2-\sqrt{3}}}=\sqrt{\frac{(2+\sqrt{3})(2+\sqrt{3})}{(2-\sqrt{3})(2+\sqrt{3})}}\) \(=\frac{2+\sqrt{3}}{\sqrt{4-3}}=2+\sqrt{3}\) \(\therefore x^2(x-4)^2=(2+\sqrt{3})^2(2+\sqrt{3}-4)^2\) \(=(\sqrt{3}+2)^2(\sqrt{3}-2)^2\)…
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