2 (functions) · 2 (capacities) · 3 (colors)=12 combinations of options
By de Moivre's theorem,

![\implies \sqrt[4]{(1 - i)^2} = \sqrt[4]{2}\,e^{i(2\pi k-\pi/2)/4} = \sqrt[4]{2}\,e^{i(4k-1)\pi/8}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csqrt%5B4%5D%7B%281%20-%20i%29%5E2%7D%20%3D%20%5Csqrt%5B4%5D%7B2%7D%5C%2Ce%5E%7Bi%282%5Cpi%20k-%5Cpi%2F2%29%2F4%7D%20%3D%20%5Csqrt%5B4%5D%7B2%7D%5C%2Ce%5E%7Bi%284k-1%29%5Cpi%2F8%7D)
where
. The fourth roots of
are then
![k = 0 \implies \sqrt[4]{2}\,e^{-i\pi/8}](https://tex.z-dn.net/?f=k%20%3D%200%20%5Cimplies%20%5Csqrt%5B4%5D%7B2%7D%5C%2Ce%5E%7B-i%5Cpi%2F8%7D)
![k = 1 \implies \sqrt[4]{2}\,e^{i3\pi/8}](https://tex.z-dn.net/?f=k%20%3D%201%20%5Cimplies%20%5Csqrt%5B4%5D%7B2%7D%5C%2Ce%5E%7Bi3%5Cpi%2F8%7D)
![k = 2 \implies \sqrt[4]{2}\,e^{i7\pi/8}](https://tex.z-dn.net/?f=k%20%3D%202%20%5Cimplies%20%5Csqrt%5B4%5D%7B2%7D%5C%2Ce%5E%7Bi7%5Cpi%2F8%7D)
![k = 3 \implies \sqrt[4]{2}\,e^{i11\pi/8}](https://tex.z-dn.net/?f=k%20%3D%203%20%5Cimplies%20%5Csqrt%5B4%5D%7B2%7D%5C%2Ce%5E%7Bi11%5Cpi%2F8%7D)
or more simply
![\boxed{\pm\sqrt[4]{2}\,e^{-i\pi/8} \text{ and } \pm\sqrt[4]{2}\,e^{i3\pi/8}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cpm%5Csqrt%5B4%5D%7B2%7D%5C%2Ce%5E%7B-i%5Cpi%2F8%7D%20%5Ctext%7B%20and%20%7D%20%5Cpm%5Csqrt%5B4%5D%7B2%7D%5C%2Ce%5E%7Bi3%5Cpi%2F8%7D%7D)
We can go on to put these in rectangular form. Recall


Then




and the roots are equivalently
![\boxed{\pm\sqrt[4]{2}\left(\sqrt{\dfrac12 + \dfrac1{2\sqrt2}} - i\sqrt{\dfrac12 - \dfrac1{2\sqrt2}}\right) \text{ and } \pm\sqrt[4]{2}\left(\sqrt{\dfrac12 + \dfrac1{2\sqrt2}} + i \sqrt{\dfrac12 - \dfrac1{2\sqrt2}}\right)}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cpm%5Csqrt%5B4%5D%7B2%7D%5Cleft%28%5Csqrt%7B%5Cdfrac12%20%2B%20%5Cdfrac1%7B2%5Csqrt2%7D%7D%20-%20i%5Csqrt%7B%5Cdfrac12%20-%20%5Cdfrac1%7B2%5Csqrt2%7D%7D%5Cright%29%20%5Ctext%7B%20and%20%7D%20%5Cpm%5Csqrt%5B4%5D%7B2%7D%5Cleft%28%5Csqrt%7B%5Cdfrac12%20%2B%20%5Cdfrac1%7B2%5Csqrt2%7D%7D%20%2B%20i%20%5Csqrt%7B%5Cdfrac12%20-%20%5Cdfrac1%7B2%5Csqrt2%7D%7D%5Cright%29%7D)
25x² - 36 = 0
25x² - 30x + 30x - 36 = 0
5x(5x) - 5x(6) + 6(5x) - 6(6) = 0
5x(5x - 6) + 6(5x - 6) = 0
(5x + 6)(5x - 6) = 0
5x + 6 = 0 or 5x - 6 = 0
- 6 - 6 + 6 + 6
5x = -6 5x = 6
5 5 5 5
x = -1.2 x = 1.2
For example smallest x which makes inequelity is x =14
because 14 + 7 = 21 > 20
you can take any number >= 14
Answer:
x=
y=5-
Step-by-step explanation:
x+y=5
y=5-x
x-y=a
x-(5-x)=a
2x-5=a
2x=a+5
x=
x+y=5
+y=5
y=5-