Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation (a-2)(b+5)=(a-2)b+(a-2)5
-
Equation x+5=0
-
Equation 16x^2-1=0
-
Equation 3x^2-3=0
- Express {x} in terms of y where:
- -3*x-13*y=-11
- -12*x-7*y=12
- -5*x+15*y=3
- -16*x+18*y=-17
- Sum of series:
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10
- Derivative of:
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10
- Integral of d{x}:
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10
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Identical expressions
- 9x(x+ five)(x- three)= ten
- 9x(x plus 5)(x minus 3) equally 10
- 9x(x plus five)(x minus three) equally ten
- 9xx+5x-3=10
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Similar expressions
- 9x(x+5)(x+3)=10
- 9x(x-5)(x-3)=10
9x(x+5)(x-3)=10 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Rapid solution
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/ 1 \ / / ________\\ / / 1 \ / / ________\\ / / ________\\\ / / ________\\
49*re|---------------------------------------| | |\/ 101265 || | 49*im|---------------------------------------| | |\/ 101265 || | |\/ 101265 ||| | |\/ 101265 ||
| ____________________ / ___\| |atan|----------|| | | ____________________ / ___\| |atan|----------|| |atan|----------||| |atan|----------||
|3 / ________ | 1 I*\/ 3 || | \ 128 /| | |3 / ________ | 1 I*\/ 3 || | \ 128 /| ___ | \ 128 /|| ___ | \ 128 /|
|\/ 128 + I*\/ 101265 *|- - - -------|| 7*cos|----------------| | |\/ 128 + I*\/ 101265 *|- - - -------|| 7*sin|----------------| 7*\/ 3 *cos|----------------|| 7*\/ 3 *sin|----------------|
2 \ \ 2 2 // \ 3 / | \ \ 2 2 // \ 3 / \ 3 /| \ 3 /
x1 = - - - ---------------------------------------------- + ----------------------- + I*|- ---------------------------------------------- + ----------------------- + -----------------------------| - -----------------------------
3 3 6 \ 3 6 6 / 6
$$x_{1} = - \frac{7 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6} - \frac{2}{3} - \frac{49 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{128 + \sqrt{101265} i}}\right)}}{3} + \frac{7 \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6} + i \left(- \frac{49 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{128 + \sqrt{101265} i}}\right)}}{3} + \frac{7 \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6} + \frac{7 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6}\right)$$
/ 1 \ / / ________\\ / / 1 \ / / ________\\ / / ________\\\ / / ________\\
49*re|---------------------------------------| | |\/ 101265 || | 49*im|---------------------------------------| | |\/ 101265 || | |\/ 101265 ||| | |\/ 101265 ||
| ____________________ / ___\| |atan|----------|| | | ____________________ / ___\| |atan|----------|| |atan|----------||| |atan|----------||
|3 / ________ | 1 I*\/ 3 || | \ 128 /| | |3 / ________ | 1 I*\/ 3 || | \ 128 /| ___ | \ 128 /|| ___ | \ 128 /|
|\/ 128 + I*\/ 101265 *|- - + -------|| 7*cos|----------------| | |\/ 128 + I*\/ 101265 *|- - + -------|| 7*sin|----------------| 7*\/ 3 *cos|----------------|| 7*\/ 3 *sin|----------------|
2 \ \ 2 2 // \ 3 / | \ \ 2 2 // \ 3 / \ 3 /| \ 3 /
x2 = - - - ---------------------------------------------- + ----------------------- + I*|- ---------------------------------------------- + ----------------------- - -----------------------------| + -----------------------------
3 3 6 \ 3 6 6 / 6
$$x_{2} = - \frac{2}{3} + \frac{7 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6} + \frac{7 \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{128 + \sqrt{101265} i}}\right)}}{3} + i \left(- \frac{7 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6} + \frac{7 \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{128 + \sqrt{101265} i}}\right)}}{3}\right)$$
____________________
3 / ________
2 49 \/ 128 + I*\/ 101265
x3 = - - - ------------------------- - -----------------------
3 ____________________ 3
3 / ________
3*\/ 128 + I*\/ 101265
$$x_{3} = - \frac{2}{3} - \frac{\sqrt[3]{128 + \sqrt{101265} i}}{3} - \frac{49}{3 \sqrt[3]{128 + \sqrt{101265} i}}$$
x3 = -2/3 - (128 + sqrt(101265)*i)^(1/3)/3 - 49/(3*(128 + sqrt(101265)*i)^(1/3))
Sum and product of roots
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sum
/ 1 \ / / ________\\ / / 1 \ / / ________\\ / / ________\\\ / / ________\\ / 1 \ / / ________\\ / / 1 \ / / ________\\ / / ________\\\ / / ________\\
49*re|---------------------------------------| | |\/ 101265 || | 49*im|---------------------------------------| | |\/ 101265 || | |\/ 101265 ||| | |\/ 101265 || 49*re|---------------------------------------| | |\/ 101265 || | 49*im|---------------------------------------| | |\/ 101265 || | |\/ 101265 ||| | |\/ 101265 ||
| ____________________ / ___\| |atan|----------|| | | ____________________ / ___\| |atan|----------|| |atan|----------||| |atan|----------|| | ____________________ / ___\| |atan|----------|| | | ____________________ / ___\| |atan|----------|| |atan|----------||| |atan|----------||
|3 / ________ | 1 I*\/ 3 || | \ 128 /| | |3 / ________ | 1 I*\/ 3 || | \ 128 /| ___ | \ 128 /|| ___ | \ 128 /| |3 / ________ | 1 I*\/ 3 || | \ 128 /| | |3 / ________ | 1 I*\/ 3 || | \ 128 /| ___ | \ 128 /|| ___ | \ 128 /| ____________________
|\/ 128 + I*\/ 101265 *|- - - -------|| 7*cos|----------------| | |\/ 128 + I*\/ 101265 *|- - - -------|| 7*sin|----------------| 7*\/ 3 *cos|----------------|| 7*\/ 3 *sin|----------------| |\/ 128 + I*\/ 101265 *|- - + -------|| 7*cos|----------------| | |\/ 128 + I*\/ 101265 *|- - + -------|| 7*sin|----------------| 7*\/ 3 *cos|----------------|| 7*\/ 3 *sin|----------------| 3 / ________
2 \ \ 2 2 // \ 3 / | \ \ 2 2 // \ 3 / \ 3 /| \ 3 / 2 \ \ 2 2 // \ 3 / | \ \ 2 2 // \ 3 / \ 3 /| \ 3 / 2 49 \/ 128 + I*\/ 101265
- - - ---------------------------------------------- + ----------------------- + I*|- ---------------------------------------------- + ----------------------- + -----------------------------| - ----------------------------- + - - - ---------------------------------------------- + ----------------------- + I*|- ---------------------------------------------- + ----------------------- - -----------------------------| + ----------------------------- + - - - ------------------------- - -----------------------
3 3 6 \ 3 6 6 / 6 3 3 6 \ 3 6 6 / 6 3 ____________________ 3
3 / ________
3*\/ 128 + I*\/ 101265
$$\left(- \frac{2}{3} - \frac{\sqrt[3]{128 + \sqrt{101265} i}}{3} - \frac{49}{3 \sqrt[3]{128 + \sqrt{101265} i}}\right) + \left(\left(- \frac{2}{3} + \frac{7 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6} + \frac{7 \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{128 + \sqrt{101265} i}}\right)}}{3} + i \left(- \frac{7 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6} + \frac{7 \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{128 + \sqrt{101265} i}}\right)}}{3}\right)\right) + \left(- \frac{7 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6} - \frac{2}{3} - \frac{49 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{128 + \sqrt{101265} i}}\right)}}{3} + \frac{7 \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6} + i \left(- \frac{49 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{128 + \sqrt{101265} i}}\right)}}{3} + \frac{7 \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6} + \frac{7 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6}\right)\right)\right)$$
=
/ 1 \ / 1 \ / / ________\\ / / 1 \ / / ________\\ / / ________\\\ / / 1 \ / / ________\\ / / ________\\\
49*re|---------------------------------------| 49*re|---------------------------------------| | |\/ 101265 || | 49*im|---------------------------------------| | |\/ 101265 || | |\/ 101265 ||| | 49*im|---------------------------------------| | |\/ 101265 || | |\/ 101265 |||
| ____________________ / ___\| | ____________________ / ___\| |atan|----------|| | | ____________________ / ___\| |atan|----------|| |atan|----------||| | | ____________________ / ___\| |atan|----------|| |atan|----------|||
|3 / ________ | 1 I*\/ 3 || |3 / ________ | 1 I*\/ 3 || ____________________ | \ 128 /| | |3 / ________ | 1 I*\/ 3 || | \ 128 /| ___ | \ 128 /|| | |3 / ________ | 1 I*\/ 3 || | \ 128 /| ___ | \ 128 /||
|\/ 128 + I*\/ 101265 *|- - + -------|| |\/ 128 + I*\/ 101265 *|- - - -------|| 3 / ________ 7*cos|----------------| | |\/ 128 + I*\/ 101265 *|- - + -------|| 7*sin|----------------| 7*\/ 3 *cos|----------------|| | |\/ 128 + I*\/ 101265 *|- - - -------|| 7*sin|----------------| 7*\/ 3 *cos|----------------||
49 \ \ 2 2 // \ \ 2 2 // \/ 128 + I*\/ 101265 \ 3 / | \ \ 2 2 // \ 3 / \ 3 /| | \ \ 2 2 // \ 3 / \ 3 /|
-2 - ------------------------- - ---------------------------------------------- - ---------------------------------------------- - ----------------------- + ----------------------- + I*|- ---------------------------------------------- + ----------------------- - -----------------------------| + I*|- ---------------------------------------------- + ----------------------- + -----------------------------|
____________________ 3 3 3 3 \ 3 6 6 / \ 3 6 6 /
3 / ________
3*\/ 128 + I*\/ 101265
$$-2 - \frac{49 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{128 + \sqrt{101265} i}}\right)}}{3} - \frac{49 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{128 + \sqrt{101265} i}}\right)}}{3} + \frac{7 \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{3} - \frac{\sqrt[3]{128 + \sqrt{101265} i}}{3} + i \left(- \frac{7 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6} + \frac{7 \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{128 + \sqrt{101265} i}}\right)}}{3}\right) + i \left(- \frac{49 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{128 + \sqrt{101265} i}}\right)}}{3} + \frac{7 \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6} + \frac{7 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6}\right) - \frac{49}{3 \sqrt[3]{128 + \sqrt{101265} i}}$$
product
/ / 1 \ / / ________\\ / / 1 \ / / ________\\ / / ________\\\ / / ________\\\ / / 1 \ / / ________\\ / / 1 \ / / ________\\ / / ________\\\ / / ________\\\
| 49*re|---------------------------------------| | |\/ 101265 || | 49*im|---------------------------------------| | |\/ 101265 || | |\/ 101265 ||| | |\/ 101265 ||| | 49*re|---------------------------------------| | |\/ 101265 || | 49*im|---------------------------------------| | |\/ 101265 || | |\/ 101265 ||| | |\/ 101265 |||
| | ____________________ / ___\| |atan|----------|| | | ____________________ / ___\| |atan|----------|| |atan|----------||| |atan|----------||| | | ____________________ / ___\| |atan|----------|| | | ____________________ / ___\| |atan|----------|| |atan|----------||| |atan|----------|||
| |3 / ________ | 1 I*\/ 3 || | \ 128 /| | |3 / ________ | 1 I*\/ 3 || | \ 128 /| ___ | \ 128 /|| ___ | \ 128 /|| | |3 / ________ | 1 I*\/ 3 || | \ 128 /| | |3 / ________ | 1 I*\/ 3 || | \ 128 /| ___ | \ 128 /|| ___ | \ 128 /|| / ____________________\
| |\/ 128 + I*\/ 101265 *|- - - -------|| 7*cos|----------------| | |\/ 128 + I*\/ 101265 *|- - - -------|| 7*sin|----------------| 7*\/ 3 *cos|----------------|| 7*\/ 3 *sin|----------------|| | |\/ 128 + I*\/ 101265 *|- - + -------|| 7*cos|----------------| | |\/ 128 + I*\/ 101265 *|- - + -------|| 7*sin|----------------| 7*\/ 3 *cos|----------------|| 7*\/ 3 *sin|----------------|| | 3 / ________ |
| 2 \ \ 2 2 // \ 3 / | \ \ 2 2 // \ 3 / \ 3 /| \ 3 /| | 2 \ \ 2 2 // \ 3 / | \ \ 2 2 // \ 3 / \ 3 /| \ 3 /| | 2 49 \/ 128 + I*\/ 101265 |
|- - - ---------------------------------------------- + ----------------------- + I*|- ---------------------------------------------- + ----------------------- + -----------------------------| - -----------------------------|*|- - - ---------------------------------------------- + ----------------------- + I*|- ---------------------------------------------- + ----------------------- - -----------------------------| + -----------------------------|*|- - - ------------------------- - -----------------------|
\ 3 3 6 \ 3 6 6 / 6 / \ 3 3 6 \ 3 6 6 / 6 / | 3 ____________________ 3 |
| 3 / ________ |
\ 3*\/ 128 + I*\/ 101265 /
$$\left(- \frac{2}{3} + \frac{7 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6} + \frac{7 \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{128 + \sqrt{101265} i}}\right)}}{3} + i \left(- \frac{7 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6} + \frac{7 \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{128 + \sqrt{101265} i}}\right)}}{3}\right)\right) \left(- \frac{7 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6} - \frac{2}{3} - \frac{49 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{128 + \sqrt{101265} i}}\right)}}{3} + \frac{7 \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6} + i \left(- \frac{49 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{128 + \sqrt{101265} i}}\right)}}{3} + \frac{7 \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6} + \frac{7 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)}}{6}\right)\right) \left(- \frac{2}{3} - \frac{\sqrt[3]{128 + \sqrt{101265} i}}{3} - \frac{49}{3 \sqrt[3]{128 + \sqrt{101265} i}}\right)$$
=
/ / / ________\\ / / ________\\\
| | |\/ 101265 || | |\/ 101265 |||
/ ____________________ / ____________________\\ | |2*atan|----------|| |atan|----------|||
| 3 / ________ | 3 / ________ || | | \ 128 /| | \ 128 /||
\49 + \/ 128 + I*\/ 101265 *\2 + \/ 128 + I*\/ 101265 //*|180 - 392*cos|------------------| + 112*cos|----------------||
\ \ 3 / \ 3 //
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____________________
3 / ________
108*\/ 128 + I*\/ 101265
$$\frac{\left(49 + \left(2 + \sqrt[3]{128 + \sqrt{101265} i}\right) \sqrt[3]{128 + \sqrt{101265} i}\right) \left(- 392 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)} + 112 \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{101265}}{128} \right)}}{3} \right)} + 180\right)}{108 \sqrt[3]{128 + \sqrt{101265} i}}$$
(49 + (128 + i*sqrt(101265))^(1/3)*(2 + (128 + i*sqrt(101265))^(1/3)))*(180 - 392*cos(2*atan(sqrt(101265)/128)/3) + 112*cos(atan(sqrt(101265)/128)/3))/(108*(128 + i*sqrt(101265))^(1/3))
Numerical answer
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x1 = -0.0733824209696124
x2 = 3.04534979986219
x3 = -4.97196737889258
x3 = -4.97196737889258