Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation sin(x)=0
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Equation z^3=1
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Equation x^2-20=x
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Equation 4^x+3=11^x
- Express {x} in terms of y where:
- 3*x-7*y=-5
- -17*x-2*y=7
- -20*x-12*y=13
- -8*x+2*y=11
- Graphing y =:
- x-ln(x+1)
- Derivative of:
- x-ln(x+1)
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Identical expressions
- x-ln(x+ one)= one
- x minus ln(x plus 1) equally 1
- x minus ln(x plus one) equally one
- x-lnx+1=1
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Similar expressions
- x+ln(x+1)=1
- x-ln(x-1)=1
x-ln(x+1)=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Rapid solution
[src]
/ -2\ x1 = -1 - W\-e /
$$x_{1} = -1 - W\left(- \frac{1}{e^{2}}\right)$$
/ -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]
sum
/ -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/
$$-2 - W\left(- \frac{1}{e^{2}}\right) - W_{-1}\left(- \frac{1}{e^{2}}\right)$$
product
/ / -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))