Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 2x^2-x=0
-
Equation 4*x^2-13*x+3=0
-
Equation -x^2+6*x-7=0
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Equation x(x^2+6x+9)=-2(x+3)
- Express {x} in terms of y where:
- -12*x+7*y=-9
- -19*x-6*y=10
- 19*x-6*y=0
- 15*x+3*y=-16
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Identical expressions
- three ^x- nine *x+ thirteen = zero
- 3 to the power of x minus 9 multiply by x plus 13 equally 0
- three to the power of x minus nine multiply by x plus thirteen equally zero
- 3x-9*x+13=0
- 3^x-9x+13=0
- 3x-9x+13=0
- 3^x-9*x+13=O
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Similar expressions
- 3^x-9*x-13=0
- 3^x+9*x+13=0
3^x-9*x+13=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Rapid solution
[src]
/ / / 4/9\\\
| | | 3 ||| / / / 4/9\\\
| | | ----||| | | | 3 |||
| | | 3 ||| log(1594323) | | | ----|||
- re\W\-log\3 /// + ------------ | | | 3 |||
9 I*im\W\-log\3 ///
x1 = ----------------------------------- - --------------------
log(3) log(3)
$$x_{1} = \frac{- \operatorname{re}{\left(W\left(- \log{\left(3^{\frac{3^{\frac{4}{9}}}{3}} \right)}\right)\right)} + \frac{\log{\left(1594323 \right)}}{9}}{\log{\left(3 \right)}} - \frac{i \operatorname{im}{\left(W\left(- \log{\left(3^{\frac{3^{\frac{4}{9}}}{3}} \right)}\right)\right)}}{\log{\left(3 \right)}}$$
x1 = (-re(LambertW(-log(3^(3^(4/9)/3)))) + log(1594323)/9)/log(3) - i*im(LambertW(-log(3^(3^(4/9)/3))))/log(3)
Sum and product of roots
[src]
sum
/ / / 4/9\\\
| | | 3 ||| / / / 4/9\\\
| | | ----||| | | | 3 |||
| | | 3 ||| log(1594323) | | | ----|||
- re\W\-log\3 /// + ------------ | | | 3 |||
9 I*im\W\-log\3 ///
----------------------------------- - --------------------
log(3) log(3)
$$\frac{- \operatorname{re}{\left(W\left(- \log{\left(3^{\frac{3^{\frac{4}{9}}}{3}} \right)}\right)\right)} + \frac{\log{\left(1594323 \right)}}{9}}{\log{\left(3 \right)}} - \frac{i \operatorname{im}{\left(W\left(- \log{\left(3^{\frac{3^{\frac{4}{9}}}{3}} \right)}\right)\right)}}{\log{\left(3 \right)}}$$
=
/ / / 4/9\\\
| | | 3 ||| / / / 4/9\\\
| | | ----||| | | | 3 |||
| | | 3 ||| log(1594323) | | | ----|||
- re\W\-log\3 /// + ------------ | | | 3 |||
9 I*im\W\-log\3 ///
----------------------------------- - --------------------
log(3) log(3)
$$\frac{- \operatorname{re}{\left(W\left(- \log{\left(3^{\frac{3^{\frac{4}{9}}}{3}} \right)}\right)\right)} + \frac{\log{\left(1594323 \right)}}{9}}{\log{\left(3 \right)}} - \frac{i \operatorname{im}{\left(W\left(- \log{\left(3^{\frac{3^{\frac{4}{9}}}{3}} \right)}\right)\right)}}{\log{\left(3 \right)}}$$
product
/ / / 4/9\\\
| | | 3 ||| / / / 4/9\\\
| | | ----||| | | | 3 |||
| | | 3 ||| log(1594323) | | | ----|||
- re\W\-log\3 /// + ------------ | | | 3 |||
9 I*im\W\-log\3 ///
----------------------------------- - --------------------
log(3) log(3)
$$\frac{- \operatorname{re}{\left(W\left(- \log{\left(3^{\frac{3^{\frac{4}{9}}}{3}} \right)}\right)\right)} + \frac{\log{\left(1594323 \right)}}{9}}{\log{\left(3 \right)}} - \frac{i \operatorname{im}{\left(W\left(- \log{\left(3^{\frac{3^{\frac{4}{9}}}{3}} \right)}\right)\right)}}{\log{\left(3 \right)}}$$
=
/ / / 4/9\\\ / / / 4/9\\\
| | | 3 ||| | | | 3 |||
| | | ----||| | | | ----|||
| | | 3 ||| log(1594323) | | | 3 |||
- re\W\-log\3 /// + ------------ - I*im\W\-log\3 ///
9
----------------------------------------------------------
log(3)
$$\frac{- \operatorname{re}{\left(W\left(- \log{\left(3^{\frac{3^{\frac{4}{9}}}{3}} \right)}\right)\right)} + \frac{\log{\left(1594323 \right)}}{9} - i \operatorname{im}{\left(W\left(- \log{\left(3^{\frac{3^{\frac{4}{9}}}{3}} \right)}\right)\right)}}{\log{\left(3 \right)}}$$
(-re(LambertW(-log(3^(3^(4/9)/3)))) + log(1594323)/9 - i*im(LambertW(-log(3^(3^(4/9)/3)))))/log(3)
Numerical answer
[src]
x1 = 2.05795766361335 - 0.871442180113678*i
x1 = 2.05795766361335 - 0.871442180113678*i