Формула квадрата разности
a²-2ab+b²=(a-b)²
y²-4y+4=y²-2·2·y+2²=(y-2)²
![2\, cos^4x+3\, sin^2x-2=0\\\\2\, cos^4x+3\cdot (1-cos^2x)-2=0\\\\2\, cos^4x-3cos^2x+1=0\\\\t=cos^2x\geq 0\; \; ,\; \; 2t^2-3t+1=0\; ,\; \; D=1\; ,\; \; t_1=\frac{1}{2}\; ,\; \; t_2=1\\\\a)\; \; cos^2x=\frac{1}{2}\; \; \to \; \; cos^2x=\frac{1+cos2x}{2}=\frac{1}{2}\; \; ,\; \; 1+cos2x=1\; ,\\\\cos2x=0\; \; ,\; \; 2x=\frac{\pi }{2}+\pi n=\; ,\; n\in Z\\\\\underline {x=\frac{\pi}{4}+\frac{\pi n}{2}\; ,\; n\in Z}](https://tex.z-dn.net/?f=2%5C%2C%20cos%5E4x%2B3%5C%2C%20sin%5E2x-2%3D0%5C%5C%5C%5C2%5C%2C%20cos%5E4x%2B3%5Ccdot%20%281-cos%5E2x%29-2%3D0%5C%5C%5C%5C2%5C%2C%20cos%5E4x-3cos%5E2x%2B1%3D0%5C%5C%5C%5Ct%3Dcos%5E2x%5Cgeq%200%5C%3B%20%5C%3B%20%2C%5C%3B%20%5C%3B%202t%5E2-3t%2B1%3D0%5C%3B%20%2C%5C%3B%20%5C%3B%20D%3D1%5C%3B%20%2C%5C%3B%20%5C%3B%20t_1%3D%5Cfrac%7B1%7D%7B2%7D%5C%3B%20%2C%5C%3B%20%5C%3B%20t_2%3D1%5C%5C%5C%5Ca%29%5C%3B%20%5C%3B%20cos%5E2x%3D%5Cfrac%7B1%7D%7B2%7D%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%20cos%5E2x%3D%5Cfrac%7B1%2Bcos2x%7D%7B2%7D%3D%5Cfrac%7B1%7D%7B2%7D%5C%3B%20%5C%3B%20%2C%5C%3B%20%5C%3B%201%2Bcos2x%3D1%5C%3B%20%2C%5C%5C%5C%5Ccos2x%3D0%5C%3B%20%5C%3B%20%2C%5C%3B%20%5C%3B%202x%3D%5Cfrac%7B%5Cpi%20%7D%7B2%7D%2B%5Cpi%20n%3D%5C%3B%20%2C%5C%3B%20n%5Cin%20Z%5C%5C%5C%5C%5Cunderline%20%7Bx%3D%5Cfrac%7B%5Cpi%7D%7B4%7D%2B%5Cfrac%7B%5Cpi%20n%7D%7B2%7D%5C%3B%20%2C%5C%3B%20n%5Cin%20Z%7D)
![b)\; \; cos^2x=1\; \; \to \; \; \frac{1+cos2x}{2}=1\; ,\; \; 1+cos2x=2\; ,\; \; cos2x=1\; ,\\\\2x=2\pi k\; ,\; \; \underline {x=\pi k\; ,\; k\in Z}\\\\Otvet:\; \; x=\frac{\pi}{4}+\frac{\pi n}{2}\; \; ,\; \; x=\pi k\; ,\; \; n,k\in Z\; .](https://tex.z-dn.net/?f=b%29%5C%3B%20%5C%3B%20cos%5E2x%3D1%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%20%5Cfrac%7B1%2Bcos2x%7D%7B2%7D%3D1%5C%3B%20%2C%5C%3B%20%5C%3B%201%2Bcos2x%3D2%5C%3B%20%2C%5C%3B%20%5C%3B%20cos2x%3D1%5C%3B%20%2C%5C%5C%5C%5C2x%3D2%5Cpi%20k%5C%3B%20%2C%5C%3B%20%5C%3B%20%5Cunderline%20%7Bx%3D%5Cpi%20k%5C%3B%20%2C%5C%3B%20k%5Cin%20Z%7D%5C%5C%5C%5COtvet%3A%5C%3B%20%5C%3B%20x%3D%5Cfrac%7B%5Cpi%7D%7B4%7D%2B%5Cfrac%7B%5Cpi%20n%7D%7B2%7D%5C%3B%20%5C%3B%20%2C%5C%3B%20%5C%3B%20x%3D%5Cpi%20k%5C%3B%20%2C%5C%3B%20%5C%3B%20n%2Ck%5Cin%20Z%5C%3B%20.)
Можно было решить пункты а) и b) , не избавляясь от квадратов косинуса, но тогда надо объединять решения.
![cos^2x=\frac{1}{2}\; \; \to \; \; cosx=\pm \frac{1}{\sqrt2}\; \; ,\\\\a)\; \; cosx=\frac{1}{\sqrt2}\; ,\; \; x=\pm \frac{\pi}{4}+2\pi n\; ,\; n\in Z\\\\b)\; \; cosx=-\frac{1}{\sqrt2}\; \; ,\; \; x=\pm \frac{3\pi}{4}+2\pi k\; ,\; k\in Z\\\\\left[\begin{array}{l}x=\pm \frac{\pi}{4}+2\pi n\\x=\pm \frac{3\pi}{4}+2\pi k\end{array}\right\; \; \Rightarrow \; \; x=\frac{\pi}{4}+\frac{\pi m}{2}\; ,\; m\in Z](https://tex.z-dn.net/?f=cos%5E2x%3D%5Cfrac%7B1%7D%7B2%7D%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%20cosx%3D%5Cpm%20%5Cfrac%7B1%7D%7B%5Csqrt2%7D%5C%3B%20%5C%3B%20%2C%5C%5C%5C%5Ca%29%5C%3B%20%5C%3B%20cosx%3D%5Cfrac%7B1%7D%7B%5Csqrt2%7D%5C%3B%20%2C%5C%3B%20%5C%3B%20x%3D%5Cpm%20%5Cfrac%7B%5Cpi%7D%7B4%7D%2B2%5Cpi%20n%5C%3B%20%2C%5C%3B%20n%5Cin%20Z%5C%5C%5C%5Cb%29%5C%3B%20%5C%3B%20cosx%3D-%5Cfrac%7B1%7D%7B%5Csqrt2%7D%5C%3B%20%5C%3B%20%2C%5C%3B%20%5C%3B%20x%3D%5Cpm%20%5Cfrac%7B3%5Cpi%7D%7B4%7D%2B2%5Cpi%20k%5C%3B%20%2C%5C%3B%20k%5Cin%20Z%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bl%7Dx%3D%5Cpm%20%5Cfrac%7B%5Cpi%7D%7B4%7D%2B2%5Cpi%20n%5C%5Cx%3D%5Cpm%20%5Cfrac%7B3%5Cpi%7D%7B4%7D%2B2%5Cpi%20k%5Cend%7Barray%7D%5Cright%5C%3B%20%5C%3B%20%5CRightarrow%20%5C%3B%20%5C%3B%20x%3D%5Cfrac%7B%5Cpi%7D%7B4%7D%2B%5Cfrac%7B%5Cpi%20m%7D%7B2%7D%5C%3B%20%2C%5C%3B%20m%5Cin%20Z)
![cos^2x=1\; \; \to \; \; cosx=\pm 1\\\\a)\; \; cosx=1\; ,\; x=2\pi n\; ,\; n\in Z\\\\b)\; \; cosx=-1\; ,\; \; x=\pi +2\pi k\; ,\; k\in Z\\\\\left[\begin{array}{l}x=2\pi n\\x=\pi +2\pi k\end{array}\right\; \; \; \Rightarrow \; \; \; x=\pi l\; ,\; l\in Z](https://tex.z-dn.net/?f=cos%5E2x%3D1%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%20cosx%3D%5Cpm%201%5C%5C%5C%5Ca%29%5C%3B%20%5C%3B%20cosx%3D1%5C%3B%20%2C%5C%3B%20x%3D2%5Cpi%20n%5C%3B%20%2C%5C%3B%20n%5Cin%20Z%5C%5C%5C%5Cb%29%5C%3B%20%5C%3B%20cosx%3D-1%5C%3B%20%2C%5C%3B%20%5C%3B%20x%3D%5Cpi%20%2B2%5Cpi%20k%5C%3B%20%2C%5C%3B%20k%5Cin%20Z%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bl%7Dx%3D2%5Cpi%20n%5C%5Cx%3D%5Cpi%20%2B2%5Cpi%20k%5Cend%7Barray%7D%5Cright%5C%3B%20%5C%3B%20%5C%3B%20%5CRightarrow%20%5C%3B%20%5C%3B%20%5C%3B%20x%3D%5Cpi%20l%5C%3B%20%2C%5C%3B%20l%5Cin%20Z)
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6b+4c-10b+c = 5c-4b
5*(3/5)-4*0.6=3-2.4=0.6