Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x^2-9)^2+(x^2-2*x-15)^2=0
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Equation x^4-x^2-20=0
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Equation cos(0.5x)=2/√2
- Equation 0.027*x^1.052-0.078*x^0.689-(0.08*100+0.154*(3+100)*600/(24*92.55)+0.03)=0
- Express {x} in terms of y where:
- 17*x-20*y=6
- 10*x-19*y=3
- -2*x-1*y=-8
- -4*x+20*y=10
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Identical expressions
- cos(zero .5x)= two /√ two
- co sinus of e of (0.5x) equally 2 divide by √2
- co sinus of e of (zero .5x) equally two divide by √ two
- cos0.5x=2/√2
- cos(0.5x)=2 divide by √2
-
Similar expressions
- y=2cos0.5xy=xlnx
- 12/(√2/2)=x/(√3/2)
- cos(0.5*x)=0.4*ln(x)
- sqrt(cos(0.5*x-1))+1=0
cos(0.5x)=2/√2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/x\ 2
cos|-| = -----
\2/ ___
\/ 2
$$\cos{\left(\frac{x}{2} \right)} = \frac{2}{\sqrt{2}}$$
Detail solution
Given the equation
$$\cos{\left(\frac{x}{2} \right)} = \frac{2}{\sqrt{2}}$$
- this is the simplest trigonometric equation
As right part of the equation
modulo =
$$\sqrt{2} > 1$$
but cos
can no be more than 1 or less than -1
so the solution of the equation d'not exist.
$$\cos{\left(\frac{x}{2} \right)} = \frac{2}{\sqrt{2}}$$
- this is the simplest trigonometric equation
As right part of the equation
modulo =
$$\sqrt{2} > 1$$
but cos
can no be more than 1 or less than -1
so the solution of the equation d'not exist.
Sum and product of roots
[src]
sum
/ / ___\\ / / ___\\ 4*pi - 2*I*im\acos\\/ 2 // + 2*I*im\acos\\/ 2 //
$$\left(4 \pi - 2 i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt{2} \right)}\right)}\right) + \left(2 i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt{2} \right)}\right)}\right)$$
=
4*pi
$$4 \pi$$
product
/ / ___\\ / / ___\\ 4*pi - 2*I*im\acos\\/ 2 // * 2*I*im\acos\\/ 2 //
$$\left(4 \pi - 2 i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt{2} \right)}\right)}\right) * \left(2 i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt{2} \right)}\right)}\right)$$
=
/ / / ___\\\ / / ___\\ 4*\2*pi*I + im\acos\\/ 2 ///*im\acos\\/ 2 //
$$4 \left(\operatorname{im}{\left(\operatorname{acos}{\left(\sqrt{2} \right)}\right)} + 2 i \pi\right) \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt{2} \right)}\right)}$$
Rapid solution
[src]
/ / ___\\ x_1 = 4*pi - 2*I*im\acos\\/ 2 //
$$x_{1} = 4 \pi - 2 i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt{2} \right)}\right)}$$
/ / ___\\ x_2 = 2*I*im\acos\\/ 2 //
$$x_{2} = 2 i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt{2} \right)}\right)}$$
Numerical answer
[src]
x1 = 12.5663706143592 - 1.76274717403909*i
x2 = 1.76274717403909*i
x2 = 1.76274717403909*i
The graph