Let \( \mathrm{C} \) be the curve \( \mathrm{f}(\mathrm{x})=\ln ^{2...

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Let \( \mathrm{C} \) be the curve \( \mathrm{f}(\mathrm{x})=\ln ^{2} \mathrm{x}+2 \ln \mathrm{x} \) and \( \mathrm{A}(\mathrm{a}, \mathrm{f}(\mathrm{a})), \mathrm{B}(\mathrm{b}, \mathrm{f}(\mathrm{b})) \) where \( (\mathrm{a}\mathrm{b}) \) are the points of tangency of two tangents drawn from origin to the curve \( \mathrm{C} \).
\( \mathrm{P} \)
(i) Find the value of the product ab.
W
(ii) Find the number of values of \( x \) satisfying the equation \( 5 \mathrm{f}^{\prime}(\mathrm{x})-\mathrm{x} \ln 10-10=0 \).
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