if x^p + y^q =(x + y)^(p+q) prove that (dy/dx)=(y/x)


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Question Number 35246 by JOHNMASANJA last updated on 17/May/18

$i f x^{p} + y^{q} = {(x + y)}^{p + q}$ $p r o v e t h a t \frac{d y}{d x} = \frac{y}{x}$
Commented by math1967 last updated on 17/May/18

$p l z . c h e c k q u e s t i o n$ $x^{p} + y^{q} {O R x}^{p} . y^{q} ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?$
	Answered by tanmay.chaudhury50@gmail.com last updated on 18/May/18

	$\frac{d y}{y} - \frac{d x}{x} = 0$ $\int \frac{d y}{y} = \int \frac{d x}{x}$ $l n y = l n x + l n k$ $l n (\frac{y}{x}) = l n k$ $y = x k$ $n o w p u t$ $y = x k i n t h e g i v e n e x p r e s s i o n$ $L H S$ $x^{p} + y^{q}$ $x^{p} + x^{q} k^{q}$ $R H S$ ${(x + y)}^{p + q}$ ${(x + x k)}^{p + a}$ $x^{p + q} \times {(1 + k)}^{p + q}$ $s o L H S n o t e q u a l s t o R H S s o q u e s t i o n i s w r o n g$ $i t h i n k . . . .$
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