Mister Exam
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How to use it?
- Equation:
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Equation (y^4+4*y^2-12)/4=0
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Equation x^2-3x-10=0
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Equation (x-119)/(x+7)=-5
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Equation 5(x-2)^2=-6x-44
- Express {x} in terms of y where:
- -2*x-15*y=-1
- 10*x-2*y=11
- 11*x-2*y=-9
- 13*x-18*y=-17
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Identical expressions
- arctg(x)+(y)^(zero . five)
- arctg(x) plus (y) to the power of (0.5)
- arctg(x) plus (y) to the power of (zero . five)
- arctg(x)+(y)(0.5)
- arctgx+y0.5
- arctgx+y^0.5
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Similar expressions
- arctg(x)-(y)^(0.5)
arctg(x)+(y)^(0.5) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
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___ atan(x) + \/ y = 0
$$\sqrt{y} + \operatorname{atan}{\left(x \right)} = 0$$
The graph
Rapid solution
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2 2 y1 = re (atan(x)) - im (atan(x)) + 2*I*im(atan(x))*re(atan(x))
$$y_{1} = \left(\operatorname{re}{\left(\operatorname{atan}{\left(x \right)}\right)}\right)^{2} + 2 i \operatorname{re}{\left(\operatorname{atan}{\left(x \right)}\right)} \operatorname{im}{\left(\operatorname{atan}{\left(x \right)}\right)} - \left(\operatorname{im}{\left(\operatorname{atan}{\left(x \right)}\right)}\right)^{2}$$
y1 = re(atan(x))^2 + 2*i*re(atan(x))*im(atan(x)) - im(atan(x))^2
Sum and product of roots
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sum
2 2 re (atan(x)) - im (atan(x)) + 2*I*im(atan(x))*re(atan(x))
$$\left(\operatorname{re}{\left(\operatorname{atan}{\left(x \right)}\right)}\right)^{2} + 2 i \operatorname{re}{\left(\operatorname{atan}{\left(x \right)}\right)} \operatorname{im}{\left(\operatorname{atan}{\left(x \right)}\right)} - \left(\operatorname{im}{\left(\operatorname{atan}{\left(x \right)}\right)}\right)^{2}$$
=
2 2 re (atan(x)) - im (atan(x)) + 2*I*im(atan(x))*re(atan(x))
$$\left(\operatorname{re}{\left(\operatorname{atan}{\left(x \right)}\right)}\right)^{2} + 2 i \operatorname{re}{\left(\operatorname{atan}{\left(x \right)}\right)} \operatorname{im}{\left(\operatorname{atan}{\left(x \right)}\right)} - \left(\operatorname{im}{\left(\operatorname{atan}{\left(x \right)}\right)}\right)^{2}$$
product
2 2 re (atan(x)) - im (atan(x)) + 2*I*im(atan(x))*re(atan(x))
$$\left(\operatorname{re}{\left(\operatorname{atan}{\left(x \right)}\right)}\right)^{2} + 2 i \operatorname{re}{\left(\operatorname{atan}{\left(x \right)}\right)} \operatorname{im}{\left(\operatorname{atan}{\left(x \right)}\right)} - \left(\operatorname{im}{\left(\operatorname{atan}{\left(x \right)}\right)}\right)^{2}$$
=
2 2 re (atan(x)) - im (atan(x)) + 2*I*im(atan(x))*re(atan(x))
$$\left(\operatorname{re}{\left(\operatorname{atan}{\left(x \right)}\right)}\right)^{2} + 2 i \operatorname{re}{\left(\operatorname{atan}{\left(x \right)}\right)} \operatorname{im}{\left(\operatorname{atan}{\left(x \right)}\right)} - \left(\operatorname{im}{\left(\operatorname{atan}{\left(x \right)}\right)}\right)^{2}$$
re(atan(x))^2 - im(atan(x))^2 + 2*i*im(atan(x))*re(atan(x))