94 > 93
99 > 98
100 > 100 - 1
99 + 1 > 99
<span>25,3 га - 100\%</span>
1) 5x²-6x+3x²-2x = 8x²-8x - уменьшаемое
2) а) = (a-b)(2x+a)
b) = 3(x+y)-b(x+y) = (3-b)(x+y)
3) 4x*3x - (3x-1)(2x+4) = 12x² - 6x²-12x+2x+4 = 6x²-10x+4
Графиком квадратичной функции является парабола.
Парабола принимает свое наибольшее или наименьшее значение в вершине параболы.
Наибольшее, если ветви параболы направлены вниз,
Наименьшее, если ветви параболы направлены вверх
Абсцисса вершины параболы y=ax²+bx+c - точка х₀=-b/2a
Если у=<span>ax²+8x-5, то</span><span> х₀=-b/2a=-8/2а=-4/а
Подставим </span><span>х₀=-4/а и у=3 в уравнение квадратичной функции </span><span>у=ax²+8x-5, получим
</span>3=а(-4/а)²+8(<span>-4/а)-5
а=-2
</span>
![\frac{2cos(x)+sin^2(x)}{ctg(x)-sin(2x)} =tg(2x)\\\frac{2cos(x)+sin^2(x)}{\frac{cos(x)}{sin(x)} -sin(2x)} =\frac{sin(2x)}{cos(2x)} \\\frac{2cos(x)+sin^2(x)}{\frac{cos(x)-sin(x)sin(2x)}{sin(x)} } =\frac{sin(2x)}{cos(2x)} \\\frac{sin(2x)+sin^3(x)}{cos(x)-sin(x)sin(2x)} -\frac{sin(x)}{cos(x)} =0\\\frac{2sin(x)cos(x)+sin^3(x)}{\sqrt{1-sin^2(x)}-sin(x)*2sin(x)cos(x)} -\frac{sin(x)}{\sqrt{1-sin^2(x)}} =0\\ \frac{2sin(x)\sqrt{1-sin^2(x)}+sin^3(x)}{\sqrt{1-sin^2(x)}-sin(x)*2sin(x)\sqrt{1-sin^2(x)}} -\frac{sin(x)}{\sqrt{1-sin^2(x)}} =0\\sin(x)=t,-1\leq t\leq 1\\\frac{2t*\sqrt{1-t^2}+t^3}{\sqrt{1-t^2}-t*2t\sqrt{1-t^2}} -\frac{t}{\sqrt{1-t^2}} =0\\\frac{2t\sqrt{1-t^2}+t^3-t(1-t*2t)}{\sqrt{1-t^2}(1-t*2t)} =0 \\\sqrt{1-t^2} (1-t*2t)\neq 0\\\sqrt{1-t^2}\neq0\\x\neq1\\t\neq-1\\1-2x^2\neq0\\t\neq\frac{\sqrt{2}}{2}\\t\neq-\frac{\sqrt{2}}{2} \\ \sqrt{1-t^2} \geq 0\\-1\leq t\leq 1\\2t\sqrt{1-t^2} =-3t^3+t\\4t^2(1-t^2)=t^2-6t^4+9t^6\\3t^2+2t^4-9t^6=0\\t^2(3+2t^2-9t^4)=0\\t^2=0\\3+2t^2-9t^4=0\\t^2=y\\3+2y-9y^2=0\\9y^2-2y-3=0\\D_1=1+27=28\\y_1=\frac{1+\sqrt{28}}{9} \\y_2=\frac{1-\sqrt{28}}{9} \\t_2=\frac{\sqrt{1+\sqrt{28}}}{3} \\t_3=-\frac{\sqrt{1+\sqrt{28}}}{3} \\\frac{1-\sqrt{28}}{9} =(-0,5) ;5<\sqrt{28} <6 =>\sqrt{28} =(5,5)=>\frac{1-5,5}{9}=(-0,5)\\t_1=0\\t_2=\frac{\sqrt{1+5,5}}{3} =\frac{\sqrt{6,5}}{3} ;2<\sqrt{6,5}<3 =>\sqrt{6,5} =2,1\\ \frac{2,1}{3}=0,7\\-\frac{\sqrt{1+5,5}}{3} =-0,7 \\ODZ:\\-1<t<-\frac{\sqrt{2}}{2};-\frac{\sqrt{2}}{2} <t<\frac{\sqrt{2}}{2} ;\frac{\sqrt{2}}{2 <t<1](https://tex.z-dn.net/?f=+%5Cfrac%7B2cos%28x%29%2Bsin%5E2%28x%29%7D%7Bctg%28x%29-sin%282x%29%7D+%3Dtg%282x%29%5C%5C%5Cfrac%7B2cos%28x%29%2Bsin%5E2%28x%29%7D%7B%5Cfrac%7Bcos%28x%29%7D%7Bsin%28x%29%7D+-sin%282x%29%7D+%3D%5Cfrac%7Bsin%282x%29%7D%7Bcos%282x%29%7D+%5C%5C%5Cfrac%7B2cos%28x%29%2Bsin%5E2%28x%29%7D%7B%5Cfrac%7Bcos%28x%29-sin%28x%29sin%282x%29%7D%7Bsin%28x%29%7D+%7D+%3D%5Cfrac%7Bsin%282x%29%7D%7Bcos%282x%29%7D++%5C%5C%5Cfrac%7Bsin%282x%29%2Bsin%5E3%28x%29%7D%7Bcos%28x%29-sin%28x%29sin%282x%29%7D+-%5Cfrac%7Bsin%28x%29%7D%7Bcos%28x%29%7D+%3D0%5C%5C%5Cfrac%7B2sin%28x%29cos%28x%29%2Bsin%5E3%28x%29%7D%7B%5Csqrt%7B1-sin%5E2%28x%29%7D-sin%28x%29%2A2sin%28x%29cos%28x%29%7D+-%5Cfrac%7Bsin%28x%29%7D%7B%5Csqrt%7B1-sin%5E2%28x%29%7D%7D+++%3D0%5C%5C+%5Cfrac%7B2sin%28x%29%5Csqrt%7B1-sin%5E2%28x%29%7D%2Bsin%5E3%28x%29%7D%7B%5Csqrt%7B1-sin%5E2%28x%29%7D-sin%28x%29%2A2sin%28x%29%5Csqrt%7B1-sin%5E2%28x%29%7D%7D+-%5Cfrac%7Bsin%28x%29%7D%7B%5Csqrt%7B1-sin%5E2%28x%29%7D%7D++%3D0%5C%5Csin%28x%29%3Dt%2C-1%5Cleq+t%5Cleq+1%5C%5C%5Cfrac%7B2t%2A%5Csqrt%7B1-t%5E2%7D%2Bt%5E3%7D%7B%5Csqrt%7B1-t%5E2%7D-t%2A2t%5Csqrt%7B1-t%5E2%7D%7D++-%5Cfrac%7Bt%7D%7B%5Csqrt%7B1-t%5E2%7D%7D++++%3D0%5C%5C%5Cfrac%7B2t%5Csqrt%7B1-t%5E2%7D%2Bt%5E3-t%281-t%2A2t%29%7D%7B%5Csqrt%7B1-t%5E2%7D%281-t%2A2t%29%7D+%3D0++%5C%5C%5Csqrt%7B1-t%5E2%7D+%281-t%2A2t%29%5Cneq+0%5C%5C%5Csqrt%7B1-t%5E2%7D%5Cneq0%5C%5Cx%5Cneq1%5C%5Ct%5Cneq-1%5C%5C1-2x%5E2%5Cneq0%5C%5Ct%5Cneq%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%5C%5Ct%5Cneq-%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D+%5C%5C+%5Csqrt%7B1-t%5E2%7D+%5Cgeq+0%5C%5C-1%5Cleq+t%5Cleq+1%5C%5C2t%5Csqrt%7B1-t%5E2%7D+%3D-3t%5E3%2Bt%5C%5C4t%5E2%281-t%5E2%29%3Dt%5E2-6t%5E4%2B9t%5E6%5C%5C3t%5E2%2B2t%5E4-9t%5E6%3D0%5C%5Ct%5E2%283%2B2t%5E2-9t%5E4%29%3D0%5C%5Ct%5E2%3D0%5C%5C3%2B2t%5E2-9t%5E4%3D0%5C%5Ct%5E2%3Dy%5C%5C3%2B2y-9y%5E2%3D0%5C%5C9y%5E2-2y-3%3D0%5C%5CD_1%3D1%2B27%3D28%5C%5Cy_1%3D%5Cfrac%7B1%2B%5Csqrt%7B28%7D%7D%7B9%7D+%5C%5Cy_2%3D%5Cfrac%7B1-%5Csqrt%7B28%7D%7D%7B9%7D+++%5C%5Ct_2%3D%5Cfrac%7B%5Csqrt%7B1%2B%5Csqrt%7B28%7D%7D%7D%7B3%7D+++%5C%5Ct_3%3D-%5Cfrac%7B%5Csqrt%7B1%2B%5Csqrt%7B28%7D%7D%7D%7B3%7D+%5C%5C%5Cfrac%7B1-%5Csqrt%7B28%7D%7D%7B9%7D+%3D%28-0%2C5%29+%3B5%3C%5Csqrt%7B28%7D++%3C6+%3D%3E%5Csqrt%7B28%7D+%3D%285%2C5%29%3D%3E%5Cfrac%7B1-5%2C5%7D%7B9%7D%3D%28-0%2C5%29%5C%5Ct_1%3D0%5C%5Ct_2%3D%5Cfrac%7B%5Csqrt%7B1%2B5%2C5%7D%7D%7B3%7D+++%3D%5Cfrac%7B%5Csqrt%7B6%2C5%7D%7D%7B3%7D++%3B2%3C%5Csqrt%7B6%2C5%7D%3C3++%3D%3E%5Csqrt%7B6%2C5%7D+%3D2%2C1%5C%5C+%5Cfrac%7B2%2C1%7D%7B3%7D%3D0%2C7%5C%5C-%5Cfrac%7B%5Csqrt%7B1%2B5%2C5%7D%7D%7B3%7D+++%3D-0%2C7+%5C%5CODZ%3A%5C%5C-1%3Ct%3C-%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%3B-%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D++%3Ct%3C%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D++%3B%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2++%3Ct%3C1++)
0,7 и -0,7 ∉ ОДЗ
t=0\\ [/tex] sin(x)=0\x=\pi k [/tex]
k∈Z
[/tex] ODZ:cos(x)cos(2x)-sin(x)sin(2x)cos(2x)\neq 0\\cos(2x)(cos(x)-sin(x)sin(2x))\neq 0\\cos(2x)\neq 0\\x\neq \frac{\pi}{4} +\frac{\pi k}{2} \\cos(x)-sin(x)sin(2x)\neq 0\\cos(x)-2sin^2(x)cos(x)\neq 0\\cos(x)(1-2sin^2(x))\neq =0\\cos(x)\neq 0\\x\neq \frac{\pi}{2} +\pi k\\1-2sin^2(x)=0\\cos(2x)\neq 0\\x\neq \frac{\pi}{4} +\frac{\pi k}{2} \\x\neq \left \{ {{\frac{\pi}{4}+\frac{\pi k}{2} } \atop {\frac{\pi}{2} }+\pi k} \right. [/tex]
Первое ОДЗ было сделано на t .Второе ОДЗ было сделано на x
Ответ:x=πk,k∈Z