JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The number of real roots of the equation \(\sqrt{x^2-4 x+3}+\sqrt{x^2-9}=\sqrt{4 x^2-14 x+6}\), is:
- A \(0\)
- B \(1\)
- C \(3\)
- D \(2\)
Answer & Solution
Correct Answer
(B) \(1\)
Step-by-step Solution
Detailed explanation
\(\sqrt{(x-1)(x-3)}+\sqrt{(x-3)(x+3)}\) \(=\sqrt{4\left(x-\frac{12}{4}\right)\left(x-\frac{2}{4}\right)}\) \(\Rightarrow \sqrt{x-3}=0 \Rightarrow x=3 \text { which is in domain }\) or \(\sqrt{x-1}+\sqrt{x+3}=\sqrt{4 x-2}\) \(2 \sqrt{(x-1)(x+3)}=2 x-4\) \(x^2+2 x-3=x^2-4 x+4\)…
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