248+226-137= 337(ор.)- собрал четвертый
248+374+226+337=1185(ор)
Ответ: все вместе они собрали 1185 орехов
0.6x + 4.2=0.5x-1.5+6.8
0.1x=1.1
x=11
2) 8/3:10/3=x/3.5
8/10=x/3.5
x=2.8
![3cos2x+sin2x-cos6x+sin6x=0\\\\2cos2x+(\underbrace {cos2x-cos6x}_{2sin2x\cdot sin4x})+(\underbrace {sin2x+sin6x}_{2sin4x\cdot cos2x})=0\, |:2\\\\cos2x+sin2x\cdot sin4x+sin4x\cdot cos2x=0\\\\cos2x+sin2x\cdot 2sin2x\cdot cos2x+sin4x\cdot cos2x=0\\\\cos2x\cdot (1+2sin^22x+sin4x)=0\\\\a)\; \; cos2x=0\; ,\; \; 2x=\frac{\pi}{2}+\pi n,\; \; x=\frac{\pi}{4}+\frac{\pi n}{2}\; ,\; n\in Z\\\\b)\; \; 1+2sin^22x+sin4x=0\\\\2sin^22x+(\underbrace {sin^22x+cos^22x}_{1})+\underbrace {2sin2x\cdot cos2x}_{sin4x}=0\\\\\underbrace {2sin^22x}_{\geq 0}+\underbrace {(sin2x+cos2x)^2}_{\geq 0}=0\; \; \Rightarrow](https://tex.z-dn.net/?f=3cos2x%2Bsin2x-cos6x%2Bsin6x%3D0%5C%5C%5C%5C2cos2x%2B%28%5Cunderbrace+%7Bcos2x-cos6x%7D_%7B2sin2x%5Ccdot+sin4x%7D%29%2B%28%5Cunderbrace+%7Bsin2x%2Bsin6x%7D_%7B2sin4x%5Ccdot+cos2x%7D%29%3D0%5C%2C+%7C%3A2%5C%5C%5C%5Ccos2x%2Bsin2x%5Ccdot+sin4x%2Bsin4x%5Ccdot+cos2x%3D0%5C%5C%5C%5Ccos2x%2Bsin2x%5Ccdot+2sin2x%5Ccdot+cos2x%2Bsin4x%5Ccdot+cos2x%3D0%5C%5C%5C%5Ccos2x%5Ccdot+%281%2B2sin%5E22x%2Bsin4x%29%3D0%5C%5C%5C%5Ca%29%5C%3B+%5C%3B+cos2x%3D0%5C%3B+%2C%5C%3B+%5C%3B+2x%3D%5Cfrac%7B%5Cpi%7D%7B2%7D%2B%5Cpi+n%2C%5C%3B+%5C%3B+x%3D%5Cfrac%7B%5Cpi%7D%7B4%7D%2B%5Cfrac%7B%5Cpi+n%7D%7B2%7D%5C%3B+%2C%5C%3B+n%5Cin+Z%5C%5C%5C%5Cb%29%5C%3B+%5C%3B+1%2B2sin%5E22x%2Bsin4x%3D0%5C%5C%5C%5C2sin%5E22x%2B%28%5Cunderbrace+%7Bsin%5E22x%2Bcos%5E22x%7D_%7B1%7D%29%2B%5Cunderbrace+%7B2sin2x%5Ccdot+cos2x%7D_%7Bsin4x%7D%3D0%5C%5C%5C%5C%5Cunderbrace+%7B2sin%5E22x%7D_%7B%5Cgeq+0%7D%2B%5Cunderbrace+%7B%28sin2x%2Bcos2x%29%5E2%7D_%7B%5Cgeq+0%7D%3D0%5C%3B+%5C%3B+%5CRightarrow+)
Сумма двух неотрицательных выражений равна нулю, если каждое выражение обращается в ноль.
![sin^22x=0\; \; \to \; \; sin2x=0\; ,\; \; 2x=\pi k,\; x=\frac{\pi k}{2}\; ,\; k\in Z\\\\(sin2x+cos2x)^2=0\; \to \; sin2x+cos2x=0\, |:cos2x\ne 0\\\\tg2x=-1\; ,\; \; 2x=-\frac{\pi}{4}+\pi m\; ,\; x=-\frac{\pi}{8}+\frac{\pi m}{2}\; ,\; m\in Z\\\\Otvet:\; \; \frac{\pi }{4}+\frac{\pi n}{2}\; ;\; \frac{\pi k}{2}\; ;\; -\frac{\pi }{8}+\frac{\pi m}{2}\; ,\; \; n,k,m\in Z\; .](https://tex.z-dn.net/?f=sin%5E22x%3D0%5C%3B+%5C%3B+%5Cto+%5C%3B+%5C%3B+sin2x%3D0%5C%3B+%2C%5C%3B+%5C%3B+2x%3D%5Cpi+k%2C%5C%3B+x%3D%5Cfrac%7B%5Cpi+k%7D%7B2%7D%5C%3B+%2C%5C%3B+k%5Cin+Z%5C%5C%5C%5C%28sin2x%2Bcos2x%29%5E2%3D0%5C%3B+%5Cto+%5C%3B+sin2x%2Bcos2x%3D0%5C%2C+%7C%3Acos2x%5Cne+0%5C%5C%5C%5Ctg2x%3D-1%5C%3B+%2C%5C%3B+%5C%3B+2x%3D-%5Cfrac%7B%5Cpi%7D%7B4%7D%2B%5Cpi+m%5C%3B+%2C%5C%3B+x%3D-%5Cfrac%7B%5Cpi%7D%7B8%7D%2B%5Cfrac%7B%5Cpi+m%7D%7B2%7D%5C%3B+%2C%5C%3B+m%5Cin+Z%5C%5C%5C%5COtvet%3A%5C%3B+%5C%3B+%5Cfrac%7B%5Cpi+%7D%7B4%7D%2B%5Cfrac%7B%5Cpi+n%7D%7B2%7D%5C%3B+%3B%5C%3B+%5Cfrac%7B%5Cpi+k%7D%7B2%7D%5C%3B+%3B%5C%3B+-%5Cfrac%7B%5Cpi+%7D%7B8%7D%2B%5Cfrac%7B%5Cpi+m%7D%7B2%7D%5C%3B+%2C%5C%3B+%5C%3B+n%2Ck%2Cm%5Cin+Z%5C%3B+.)