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  4. Sum of the squares of the distinct roots of the equation log 2 x ⋅ log 3 x ⋅ log 5 x= log 2 x ⋅ log 3 x+ log 3 x ⋅ log 5 x+ log 5 x ⋅ log 2 x

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Q. Sum of the squares of the distinct roots of the equation $\log _2 x \cdot \log _3 x \cdot \log _5 x=\log _2 x \cdot \log _3 x+\log _3 x \cdot \log _5 x+\log _5 x \cdot \log _2 x$

Continuity and Differentiability

Solution:

Roots of equation
$x = 1, 30$
Sum of squares$ = 1 + 900 = 901$