solv: e^x +x+1=0


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Question Number 167696 by bounhome last updated on 23/Mar/22

$s o l v :$ $e^{x} + x + 1 = 0$
	Answered by mr W last updated on 23/Mar/22

	$e^{x} = - (x + 1)$ $e^{x + 1} = - e (x + 1)$ $- (x + 1) e^{- (x + 1)} = \frac{1}{e}$ $- (x + 1) = W (\frac{1}{e})$ $\Rightarrow x = - 1 - W (\frac{1}{e}) \approx - 1.278465$
	Commented by essojean last updated on 25/Mar/22

	$Q u e r e p r e s e n t e W ? ? ?$
	Commented by mr W last updated on 25/Mar/22

	$L a m b e r t W f u n c t i o n$
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