(3х^2 +4)^2 -10(3х^2 +4)+21=0
Пусть у=3х^2 +4, тогда:
у^2 -10у+21=0
D=100-84=16
у1=(10-4)/2=6/2=3
у2=(10+4)/2=14/2=7
3=3х^2 +4
3х^2=3-4
х^2=-1/3 - квадрат любого числа не должен быть отрицательным.
7=3х^2 +4
3х^2=7-4
х^2=3/3
х=1
![2sin^2x=\sqrt3cos(\frac{\pi}{2}+x)](https://tex.z-dn.net/?f=2sin%5E2x%3D%5Csqrt3cos%28%5Cfrac%7B%5Cpi%7D%7B2%7D%2Bx%29)
![2sin^2x=-\sqrt3sinx](https://tex.z-dn.net/?f=2sin%5E2x%3D-%5Csqrt3sinx)
![2sin^2x+\sqrt{3}sinx=0](https://tex.z-dn.net/?f=2sin%5E2x%2B%5Csqrt%7B3%7Dsinx%3D0)
![sinx(2sinx+\sqrt3)=0](https://tex.z-dn.net/?f=sinx%282sinx%2B%5Csqrt3%29%3D0)
![sinx=0](https://tex.z-dn.net/?f=sinx%3D0)
, n∈Z
![sinx=-\frac{\sqrt3}{2}](https://tex.z-dn.net/?f=sinx%3D-%5Cfrac%7B%5Csqrt3%7D%7B2%7D)
, n∈Z
, n∈Z
Отберем корни на промежутке ![[\frac{3\pi}{2};3\pi]=[1,5\pi;3\pi]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B3%5Cpi%7D%7B2%7D%3B3%5Cpi%5D%3D%5B1%2C5%5Cpi%3B3%5Cpi%5D)
<u><em>1 случай:</em></u>
, n∈Z
∈![[1,5\pi;3\pi]](https://tex.z-dn.net/?f=%5B1%2C5%5Cpi%3B3%5Cpi%5D)
∈![[1,5\pi;3\pi]](https://tex.z-dn.net/?f=%5B1%2C5%5Cpi%3B3%5Cpi%5D)
∉![[1,5\pi;3\pi]](https://tex.z-dn.net/?f=%5B1%2C5%5Cpi%3B3%5Cpi%5D)
<u><em>2 случай:</em></u>
, n∈Z
∉![[1,5\pi;3\pi]](https://tex.z-dn.net/?f=%5B1%2C5%5Cpi%3B3%5Cpi%5D)
∈![[1,5\pi;3\pi]](https://tex.z-dn.net/?f=%5B1%2C5%5Cpi%3B3%5Cpi%5D)
∉![[1,5\pi;3\pi]](https://tex.z-dn.net/?f=%5B1%2C5%5Cpi%3B3%5Cpi%5D)
<em><u>3 случай:</u></em>
, n∈Z
∈![[1,5\pi;3\pi]](https://tex.z-dn.net/?f=%5B1%2C5%5Cpi%3B3%5Cpi%5D)
∈![[1,5\pi;3\pi]](https://tex.z-dn.net/?f=%5B1%2C5%5Cpi%3B3%5Cpi%5D)
<em>Ответ:</em>
<em><u>а) корни уравнения</u></em>:
, n∈Z
, n∈Z
, n∈Z
<u><em>б) корни лежащие в данном промежутке</em></u>
:
;
;
;
;[/tex]\frac{5\pi}{3}[/tex]
<span>0,5•0,05•0,005=0.000125....................</span>