Q15 of 29 Page 1

If then prove that x(x+1)2y2+(x+1)2y1=2

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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