Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation tgx=-1
-
Equation 2x^2-7x+6=0
-
Equation lnx+1-2x=0
- Equation ((x+6)/(x+5))+((10)/((x^2)-25))=5/4
- Express {x} in terms of y where:
- 10*x-1*y=10
- 15*x-17*y=19
- 9*x-8*y=6
- 15*x+15*y=16
-
Identical expressions
- lnx+ one -2x= zero
- lnx plus 1 minus 2x equally 0
- lnx plus one minus 2x equally zero
- lnx+1-2x=O
-
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