Q. 154.0( 4 Votes )

# If <span lang="EN

To prove that x(x+1)2y2+(x+1)2y1 = 2

We will use and

We know that log(a/b) = log a – log b

y = log (x + 1)2 – log x

As log xn = n log x

y = 2 log (x + 1) – log x

Differentiate with respect to x

Differentiate again with respect to x

Using u/v rule

Multiply (x+1) to both numerator and denominator in to get,

Using (i)

y2(x + 1)2x = 2 – (x + 1)2y1

y2(x + 1)2x + (x + 1)2y1 = 2

Hence proved

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