Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^3+2x^2-x-2=0
-
Equation 8*x=2
-
Equation -sin(x)=0
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Equation -8x-17=3x-105
- Express {x} in terms of y where:
- 15*x+10*y=-4
- 12*x-20*y=10
- -11*x-1*y=15
- 5*x-4*y=-2
-
Identical expressions
- lg²(x²)-lg(x²)= four
- lg²(x²) minus lg(x²) equally 4
- lg²(x²) minus lg(x²) equally four
- lg²x²-lgx²=4
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Similar expressions
- lg²(x²)+lg(x²)=4
lg²(x²)-lg(x²)=4 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2/ 2\ / 2\ log \x / - log\x / = 4
$$\log{\left(x^{2} \right)}^{2} - \log{\left(x^{2} \right)} = 4$$
Sum and product of roots
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sum
____ ____ ____ ____ 1 \/ 17 1 \/ 17 1 \/ 17 1 \/ 17 - - ------ - - ------ - + ------ - + ------ 4 4 4 4 4 4 4 4 - e + e - e + e
$$\left(- e^{\frac{1}{4} + \frac{\sqrt{17}}{4}} + \left(- \frac{1}{e^{- \frac{1}{4} + \frac{\sqrt{17}}{4}}} + e^{\frac{1}{4} - \frac{\sqrt{17}}{4}}\right)\right) + e^{\frac{1}{4} + \frac{\sqrt{17}}{4}}$$
=
0
$$0$$
product
____ ____ / ____\ ____ 1 \/ 17 1 \/ 17 | 1 \/ 17 | 1 \/ 17 - - ------ - - ------ | - + ------| - + ------ 4 4 4 4 | 4 4 | 4 4 -e *e *\-e /*e
$$\frac{\left(-1\right) e^{\frac{1}{4} - \frac{\sqrt{17}}{4}}}{e^{- \frac{1}{4} + \frac{\sqrt{17}}{4}}} \left(- e^{\frac{1}{4} + \frac{\sqrt{17}}{4}}\right) e^{\frac{1}{4} + \frac{\sqrt{17}}{4}}$$
=
E
$$e$$
E
Rapid solution
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____
1 \/ 17
- - ------
4 4
x1 = -e
$$x_{1} = - \frac{1}{e^{- \frac{1}{4} + \frac{\sqrt{17}}{4}}}$$
____
1 \/ 17
- - ------
4 4
x2 = e
$$x_{2} = e^{\frac{1}{4} - \frac{\sqrt{17}}{4}}$$
____
1 \/ 17
- + ------
4 4
x3 = -e
$$x_{3} = - e^{\frac{1}{4} + \frac{\sqrt{17}}{4}}$$
____
1 \/ 17
- + ------
4 4
x4 = e
$$x_{4} = e^{\frac{1}{4} + \frac{\sqrt{17}}{4}}$$
x4 = exp(1/4 + sqrt(17)/4)
Numerical answer
[src]
x1 = -0.458050240071628
x2 = 0.458050240071628
x3 = -3.59943326400682
x4 = 3.59943326400682
x4 = 3.59943326400682