x-ln(x+1)=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
$$x_{1} = -1 - W\left(- \frac{1}{e^{2}}\right)$$
/ -2 \
x2 = -1 - W\-e , -1/
$$x_{2} = -1 - W_{-1}\left(- \frac{1}{e^{2}}\right)$$
x2 = -1 - LambertW(-exp(-2, -1))
Sum and product of roots
[src]
/ -2\ / -2 \
-1 - W\-e / + -1 - W\-e , -1/
$$\left(-1 - W\left(- \frac{1}{e^{2}}\right)\right) + \left(-1 - W_{-1}\left(- \frac{1}{e^{2}}\right)\right)$$
/ -2\ / -2 \
-2 - W\-e / - W\-e , -1/
$$-2 - W\left(- \frac{1}{e^{2}}\right) - W_{-1}\left(- \frac{1}{e^{2}}\right)$$
/ / -2\\ / / -2 \\
\-1 - W\-e //*\-1 - W\-e , -1//
$$\left(-1 - W\left(- \frac{1}{e^{2}}\right)\right) \left(-1 - W_{-1}\left(- \frac{1}{e^{2}}\right)\right)$$
/ / -2\\ / / -2 \\
\1 + W\-e //*\1 + W\-e , -1//
$$\left(W\left(- \frac{1}{e^{2}}\right) + 1\right) \left(W_{-1}\left(- \frac{1}{e^{2}}\right) + 1\right)$$
(1 + LambertW(-exp(-2)))*(1 + LambertW(-exp(-2), -1))