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Question
If xy − loge y = 1 satisfies the equation \[x\left( y y_2 + y_1^2 \right) - y_2 + \lambda y y_1 = 0\]
Options
−3
1
3
none of these
Solution
(c) 3
Here,
\[xy - \log_e y = 1\]
\[ \Rightarrow x y_1 + y - \frac{y_1}{y} = 0\]
\[ \Rightarrow xy y_1 + y^2 - y_1 = 0\]
\[ \Rightarrow y y_1 + x y_1 y_1 + xy y_2 + 2y y_1 - y_2 = 0\]
\[ \Rightarrow x\left( {y_1}^2 + y y_2 \right) - y_2 + 3y y_1 = 0\]
\[ \therefore \lambda = 3\]
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