WBJEE · Maths · Basic of Mathematics
The equation \(x \log x=3-x\)
- A has no root in (1,3)
- B has exactly one root in (1,3)
- C \(x \log x-(3-x)>0\) in [1,3]
- D \(x \log x-(3-x) < 0\) in [1,3]
Answer & Solution
Correct Answer
(B) has exactly one root in (1,3)
Step-by-step Solution
Detailed explanation
Let \(\quad f(x)=x \log x+x-3\) \(\Rightarrow \quad f^{\prime}(x)=x \cdot \frac{1}{x}+\log x+1\) \(\Rightarrow \quad f^{\prime}(x)=\log x+2>0\) \(\Rightarrow f(1)=-2\) and \(f(3)=3 \log 3, f(1) \cdot f(3 0\)
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