E(cosx)=[-1;1]
E(cos2x)=[-1;1]
E(4cos2x)=[-4;4]
E(4cos2x+3)=[-1;7] => у(наиб.)=7
Объяснение:
![\sqrt{4^3} =\sqrt{4^2\cdot4} =\sqrt{4^2} \cdot \sqrt{4} = 4 \cdot 2= 8](https://tex.z-dn.net/?f=%5Csqrt%7B4%5E3%7D%20%3D%5Csqrt%7B4%5E2%5Ccdot4%7D%20%3D%5Csqrt%7B4%5E2%7D%20%5Ccdot%20%5Csqrt%7B4%7D%20%3D%204%20%5Ccdot%202%3D%208)
Ну или можно было записать, что ![\sqrt{4^3}=\sqrt{(2^3)^2}=2^3=8](https://tex.z-dn.net/?f=%5Csqrt%7B4%5E3%7D%3D%5Csqrt%7B%282%5E3%29%5E2%7D%3D2%5E3%3D8)
1) 4х-3х=7+3
1х=10
х=10
остальные не знаю
№1
![5\sqrt[4]{81}+2\sqrt[1]{125}*\sqrt[5]{243}-\sqrt{49} = 5*3+2*125*3-7 = 15+750-7 = 758\\](https://tex.z-dn.net/?f=5%5Csqrt%5B4%5D%7B81%7D%2B2%5Csqrt%5B1%5D%7B125%7D%2A%5Csqrt%5B5%5D%7B243%7D-%5Csqrt%7B49%7D+%C2%A0+%C2%A0%3D+5%2A3%2B2%2A125%2A3-7+%3D+15%2B750-7+%3D+758%5C%5C)
№2
![y^{7/3} *\sqrt[3]{y^{2} } = y^{7/3} *y^{2/3}= y^{14/3}= y^{4.. 2/3}](https://tex.z-dn.net/?f=y%5E%7B7%2F3%7D+%2A%5Csqrt%5B3%5D%7By%5E%7B2%7D+%7D+%3D+y%5E%7B7%2F3%7D+%2Ay%5E%7B2%2F3%7D%3D+y%5E%7B14%2F3%7D%3D+y%5E%7B4..+2%2F3%7D)
там, где 4..2/3, 4 - целая часть
№3
![\sqrt[3]{3x+116} =5\\3x+116=5^{3} \\3x+116=125\\3x=125-116\\3x=9\\x=3](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B3x%2B116%7D+%3D5%5C%5C3x%2B116%3D5%5E%7B3%7D+%5C%5C3x%2B116%3D125%5C%5C3x%3D125-116%5C%5C3x%3D9%5C%5Cx%3D3)
№4
прикреплен файл
№5
![5^{2x} = 625\\5^{x}=\sqrt{625}\\5^{x}=25\\x=2](https://tex.z-dn.net/?f=5%5E%7B2x%7D+%3D+625%5C%5C5%5E%7Bx%7D%3D%5Csqrt%7B625%7D%5C%5C5%5E%7Bx%7D%3D25%5C%5Cx%3D2)
№6
![2^{5x-4} =16^{x+3}\\2^{5x-4} =2^{4*(x+3)}\\2^{5x-4} =2^{4x+12}\\5x-4=4x+12\\x=16\\](https://tex.z-dn.net/?f=2%5E%7B5x-4%7D+%3D16%5E%7Bx%2B3%7D%5C%5C2%5E%7B5x-4%7D+%3D2%5E%7B4%2A%28x%2B3%29%7D%5C%5C2%5E%7B5x-4%7D+%3D2%5E%7B4x%2B12%7D%5C%5C5x-4%3D4x%2B12%5C%5Cx%3D16%5C%5C)
Ответ: в
№7
![4^{6x-3} \leq 1\\ 4^{6x}*4^{-3}\leq 1\\\frac{4096^{x}}{64} \leq 1\\4096^{x}\leq 64\\](https://tex.z-dn.net/?f=4%5E%7B6x-3%7D+%5Cleq+1%5C%5C+4%5E%7B6x%7D%2A4%5E%7B-3%7D%5Cleq+1%5C%5C%5Cfrac%7B4096%5E%7Bx%7D%7D%7B64%7D+%5Cleq+1%5C%5C4096%5E%7Bx%7D%5Cleq+64%5C%5C)
x∈(-∞; 0.5]
Ответ: б
№8
![4^{2,5} -(1/9)^{-1,5} +(5/4)^{2\3,5} *(0.8)^{3.5} = \sqrt{4^{2}} -\sqrt{9} +(\frac{\sqrt{125} }{\sqrt{64} })*\sqrt{0.512} = 4-3+\frac{\sqrt{125}*\sqrt{0.512} }{8} = 1+\frac{64}{8} = 1+8=9](https://tex.z-dn.net/?f=4%5E%7B2%2C5%7D+-%281%2F9%29%5E%7B-1%2C5%7D+%2B%285%2F4%29%5E%7B2%5C3%2C5%7D+%2A%280.8%29%5E%7B3.5%7D+%3D+%5Csqrt%7B4%5E%7B2%7D%7D+-%5Csqrt%7B9%7D+%2B%28%5Cfrac%7B%5Csqrt%7B125%7D+%7D%7B%5Csqrt%7B64%7D+%7D%29%2A%5Csqrt%7B0.512%7D+%3D+4-3%2B%5Cfrac%7B%5Csqrt%7B125%7D%2A%5Csqrt%7B0.512%7D+%C2%A0%7D%7B8%7D+%3D+1%2B%5Cfrac%7B64%7D%7B8%7D+%3D+1%2B8%3D9)
№9
![3^{2x}-2*3^{x}-3=0\\3^{x}=a\\a^{2}-2a-3=0\\D=4+12=16\\\sqrt{D} =4\\\\a1 = ( 2 - 4 ) : 2 = - 1 \\a2 = ( 2 + 4 ) / 2 = 3\\ a=3^{x}\\3= 3^{x}\\x=1](https://tex.z-dn.net/?f=3%5E%7B2x%7D-2%2A3%5E%7Bx%7D-3%3D0%5C%5C3%5E%7Bx%7D%3Da%5C%5Ca%5E%7B2%7D-2a-3%3D0%5C%5CD%3D4%2B12%3D16%5C%5C%5Csqrt%7BD%7D+%3D4%5C%5C%5C%5Ca1+%3D+%28+2+-+4+%29+%3A+2+%3D+-+1+%5C%5Ca2+%3D+%28+2+%2B+4+%29+%2F+2+%3D+3%5C%5C+a%3D3%5E%7Bx%7D%5C%5C3%3D+3%5E%7Bx%7D%5C%5Cx%3D1)
№10
![\left \{ {{3x=3^{2y+3} \atop {2^{5x+y}=2^{4}} \right. \\\left \{ {{x=2y+3} \atop {5x+y=4}} \right. \\\\5*(2y+3)+y=4\\10y+15+y=4\\11y=-11\\y=-1\\x=1\\](https://tex.z-dn.net/?f=%5Cleft+%5C%7B+%7B%7B3x%3D3%5E%7B2y%2B3%7D+%5Catop+%7B2%5E%7B5x%2By%7D%3D2%5E%7B4%7D%7D+%5Cright.+%5C%5C%5Cleft+%5C%7B+%7B%7Bx%3D2y%2B3%7D+%5Catop+%7B5x%2By%3D4%7D%7D+%5Cright.+%5C%5C%5C%5C5%2A%282y%2B3%29%2By%3D4%5C%5C10y%2B15%2By%3D4%5C%5C11y%3D-11%5C%5Cy%3D-1%5C%5Cx%3D1%5C%5C)
№11
![(1/7)^{2x^{2}-3x} \geq 1/49\\(1/7)^{2x^{2}-3x} \geq (1/7)^{2}\\2x^{2}-3x\leq 2\\2x^{2}-3x-2\leq 0\\D = 9+16 =25\\x1= 2\\x2 = -0.5\\](https://tex.z-dn.net/?f=%281%2F7%29%5E%7B2x%5E%7B2%7D-3x%7D+%5Cgeq+1%2F49%5C%5C%281%2F7%29%5E%7B2x%5E%7B2%7D-3x%7D+%5Cgeq+%281%2F7%29%5E%7B2%7D%5C%5C2x%5E%7B2%7D-3x%5Cleq+2%5C%5C2x%5E%7B2%7D-3x-2%5Cleq+0%5C%5CD+%3D+9%2B16+%3D25%5C%5Cx1%3D+2%5C%5Cx2+%3D+-0.5%5C%5C)
x∈[-0.5; 2]
целочисленные решения : 0; 1; 2
ответ: 3
..(58/x+4)*x(x-4) + (42/x-4)*x(x+4) = (100/x)*(x-4)(x+4)
58x^2-232x+42x^2+168x=100x^2-1600
100x^2-64x-100x^2+1600=0
-64x=-1600
x=25