Mister Exam
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- Equation:
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Identical expressions
- z=arcsin^(three)((xy)/ two)
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- z equally arc sinus of to the power of (three)((xy) divide by two)
- z=arcsin(3)((xy)/2)
- z=arcsin3xy/2
- z=arcsin^3xy/2
- z=arcsin^(3)((xy) divide by 2)
z=arcsin^(3)((xy)/2) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
3/x*y\
z = asin |---|
\ 2 /
$$z = \operatorname{asin}^{3}{\left(\frac{x y}{2} \right)}$$
Detail solution
Given the equation:
$$z = \operatorname{asin}^{3}{\left(\frac{x y}{2} \right)}$$
transform:
$$z = \operatorname{asin}^{3}{\left(\frac{x y}{2} \right)}$$
Expand brackets in the right part
We get the answer: z = asin(x*y/2)^3
$$z = \operatorname{asin}^{3}{\left(\frac{x y}{2} \right)}$$
transform:
$$z = \operatorname{asin}^{3}{\left(\frac{x y}{2} \right)}$$
Expand brackets in the right part
z = asinx*y/2^3
We get the answer: z = asin(x*y/2)^3
The graph
Rapid solution
[src]
3/ /x*y\\ / 3/ /x*y\\ 2/ /x*y\\ / /x*y\\\ 2/ /x*y\\ / /x*y\\
z1 = re |asin|---|| + I*|- im |asin|---|| + 3*re |asin|---||*im|asin|---||| - 3*im |asin|---||*re|asin|---||
\ \ 2 // \ \ \ 2 // \ \ 2 // \ \ 2 /// \ \ 2 // \ \ 2 //
$$z_{1} = i \left(3 \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)}\right)^{2} \operatorname{im}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)} - \left(\operatorname{im}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)}\right)^{3}\right) + \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)}\right)^{3} - 3 \operatorname{re}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)} \left(\operatorname{im}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)}\right)^{2}$$
z1 = i*(3*re(asin(x*y/2))^2*im(asin(x*y/2)) - im(asin(x*y/2))^3) + re(asin(x*y/2))^3 - 3*re(asin(x*y/2))*im(asin(x*y/2))^2
Sum and product of roots
[src]
sum
3/ /x*y\\ / 3/ /x*y\\ 2/ /x*y\\ / /x*y\\\ 2/ /x*y\\ / /x*y\\ re |asin|---|| + I*|- im |asin|---|| + 3*re |asin|---||*im|asin|---||| - 3*im |asin|---||*re|asin|---|| \ \ 2 // \ \ \ 2 // \ \ 2 // \ \ 2 /// \ \ 2 // \ \ 2 //
$$i \left(3 \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)}\right)^{2} \operatorname{im}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)} - \left(\operatorname{im}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)}\right)^{3}\right) + \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)}\right)^{3} - 3 \operatorname{re}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)} \left(\operatorname{im}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)}\right)^{2}$$
=
3/ /x*y\\ / 3/ /x*y\\ 2/ /x*y\\ / /x*y\\\ 2/ /x*y\\ / /x*y\\ re |asin|---|| + I*|- im |asin|---|| + 3*re |asin|---||*im|asin|---||| - 3*im |asin|---||*re|asin|---|| \ \ 2 // \ \ \ 2 // \ \ 2 // \ \ 2 /// \ \ 2 // \ \ 2 //
$$i \left(3 \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)}\right)^{2} \operatorname{im}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)} - \left(\operatorname{im}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)}\right)^{3}\right) + \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)}\right)^{3} - 3 \operatorname{re}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)} \left(\operatorname{im}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)}\right)^{2}$$
product
3/ /x*y\\ / 3/ /x*y\\ 2/ /x*y\\ / /x*y\\\ 2/ /x*y\\ / /x*y\\ re |asin|---|| + I*|- im |asin|---|| + 3*re |asin|---||*im|asin|---||| - 3*im |asin|---||*re|asin|---|| \ \ 2 // \ \ \ 2 // \ \ 2 // \ \ 2 /// \ \ 2 // \ \ 2 //
$$i \left(3 \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)}\right)^{2} \operatorname{im}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)} - \left(\operatorname{im}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)}\right)^{3}\right) + \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)}\right)^{3} - 3 \operatorname{re}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)} \left(\operatorname{im}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)}\right)^{2}$$
=
3/ /x*y\\ 2/ /x*y\\ / /x*y\\ / 2/ /x*y\\ 2/ /x*y\\\ / /x*y\\ re |asin|---|| - 3*im |asin|---||*re|asin|---|| + I*|- im |asin|---|| + 3*re |asin|---|||*im|asin|---|| \ \ 2 // \ \ 2 // \ \ 2 // \ \ \ 2 // \ \ 2 /// \ \ 2 //
$$i \left(3 \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)}\right)^{2} - \left(\operatorname{im}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)}\right)^{2}\right) \operatorname{im}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)} + \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)}\right)^{3} - 3 \operatorname{re}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)} \left(\operatorname{im}{\left(\operatorname{asin}{\left(\frac{x y}{2} \right)}\right)}\right)^{2}$$
re(asin(x*y/2))^3 - 3*im(asin(x*y/2))^2*re(asin(x*y/2)) + i*(-im(asin(x*y/2))^2 + 3*re(asin(x*y/2))^2)*im(asin(x*y/2))