Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^3-2x^2-5x+6=0
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Equation lnx+1-2x=0
- Equation 14n^3-(-8n^3)+(3n^3-11n^3)
- Equation tgx =2sinx
- Express {x} in terms of y where:
- 14*x-16*y=14
- -12*x+3*y=-9
- -10*x+18*y=6
- 9*x-18*y=6
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Identical expressions
- lnx+ one -2x= zero
- lnx plus 1 minus 2x equally 0
- lnx plus one minus 2x equally zero
- lnx+1-2x=O
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Similar expressions
- lnx+1+2x=0
- lnx-1-2x=0
lnx+1-2x=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Rapid solution
[src]
/ / -1\\ / / -1\\
re\W\-2*e // I*im\W\-2*e //
x_1 = - ------------- - ---------------
2 2
$$x_{1} = - \frac{\operatorname{re}{\left(W\left(- \frac{2}{e}\right)\right)}}{2} - \frac{i \operatorname{im}{\left(W\left(- \frac{2}{e}\right)\right)}}{2}$$
Sum and product of roots
[src]
sum
/ / -1\\ / / -1\\
re\W\-2*e // I*im\W\-2*e //
- ------------- - ---------------
2 2
$$\left(- \frac{\operatorname{re}{\left(W\left(- \frac{2}{e}\right)\right)}}{2} - \frac{i \operatorname{im}{\left(W\left(- \frac{2}{e}\right)\right)}}{2}\right)$$
=
/ / -1\\ / / -1\\
re\W\-2*e // I*im\W\-2*e //
- ------------- - ---------------
2 2
$$- \frac{\operatorname{re}{\left(W\left(- \frac{2}{e}\right)\right)}}{2} - \frac{i \operatorname{im}{\left(W\left(- \frac{2}{e}\right)\right)}}{2}$$
product
/ / -1\\ / / -1\\
re\W\-2*e // I*im\W\-2*e //
- ------------- - ---------------
2 2
$$\left(- \frac{\operatorname{re}{\left(W\left(- \frac{2}{e}\right)\right)}}{2} - \frac{i \operatorname{im}{\left(W\left(- \frac{2}{e}\right)\right)}}{2}\right)$$
=
/ / -1\\ / / -1\\
re\W\-2*e // I*im\W\-2*e //
- ------------- - ---------------
2 2
$$- \frac{\operatorname{re}{\left(W\left(- \frac{2}{e}\right)\right)}}{2} - \frac{i \operatorname{im}{\left(W\left(- \frac{2}{e}\right)\right)}}{2}$$
Numerical answer
[src]
x1 = 0.265323182170863 + 0.566336248802441*i
x1 = 0.265323182170863 + 0.566336248802441*i
The graph