Y=4x+a
x -2 -1 0 1 2
y -8+(-∞) -4+(-∞) -∞ 4+(-∞) 8+(-∞)
y -8+∞ -4+∞ ∞ 4+∞ 8+∞
Первый - во вложении
X²-y²+14y-49=x²-(y²-14y+49)=x²-(y²-2*y*7+7²)=x²-(y-7)²=(x+(y-7))(x-(y-7))=
=(x+y-7)(x-y+7)
4) ОДЗ :
![\left \{ {{x-3,5>0} \atop {x-2>0}} \right. \\\\\left \{ {{x>3,5} \atop {x>2}} \right.\Rightarrow x>3,5\\\\\\log_{7}(x-3,5)+log_{7}(x-2)<1\\\\log_{7}(x-3,5)(x-2)<log_{7}7\\\\(x-3,5)(x-2)<7\\\\x^{2}-2x-3,5x+7-7<0\\\\ x^{2}-5,5x<0\\\\x(x-5,5)<0](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7Bx-3%2C5%3E0%7D%20%5Catop%20%7Bx-2%3E0%7D%7D%20%5Cright.%20%5C%5C%5C%5C%5Cleft%20%5C%7B%20%7B%7Bx%3E3%2C5%7D%20%5Catop%20%7Bx%3E2%7D%7D%20%5Cright.%5CRightarrow%20x%3E3%2C5%5C%5C%5C%5C%5C%5Clog_%7B7%7D%28x-3%2C5%29%2Blog_%7B7%7D%28x-2%29%3C1%5C%5C%5C%5Clog_%7B7%7D%28x-3%2C5%29%28x-2%29%3Clog_%7B7%7D7%5C%5C%5C%5C%28x-3%2C5%29%28x-2%29%3C7%5C%5C%5C%5Cx%5E%7B2%7D-2x-3%2C5x%2B7-7%3C0%5C%5C%5C%5C%20x%5E%7B2%7D-5%2C5x%3C0%5C%5C%5C%5Cx%28x-5%2C5%29%3C0)
+ - +
________₀________₀_________
0 5,5
////////////////////
x ∈ (0 ; 5,5)
С учётом ОДЗ, окончательный ответ : x ∈ (3,5 ; 5,5)
![5)(\frac{625}{16})^{2x+1}\geq 0,16\\\\((\frac{5}{2})^{4})^{2x+1} \geq \frac{4}{25}\\\\(\frac{5}{2})^{8x+4}\geq(\frac{5}{2})^{-2}\\\\8x+4\geq -2\\\\8x\geq -6\\\\x\geq -0,75\\\\Otvet:\boxed{[-0,75;+\infty)}](https://tex.z-dn.net/?f=5%29%28%5Cfrac%7B625%7D%7B16%7D%29%5E%7B2x%2B1%7D%5Cgeq%200%2C16%5C%5C%5C%5C%28%28%5Cfrac%7B5%7D%7B2%7D%29%5E%7B4%7D%29%5E%7B2x%2B1%7D%20%5Cgeq%20%5Cfrac%7B4%7D%7B25%7D%5C%5C%5C%5C%28%5Cfrac%7B5%7D%7B2%7D%29%5E%7B8x%2B4%7D%5Cgeq%28%5Cfrac%7B5%7D%7B2%7D%29%5E%7B-2%7D%5C%5C%5C%5C8x%2B4%5Cgeq%20-2%5C%5C%5C%5C8x%5Cgeq%20-6%5C%5C%5C%5Cx%5Cgeq%20-0%2C75%5C%5C%5C%5COtvet%3A%5Cboxed%7B%5B-0%2C75%3B%2B%5Cinfty%29%7D)
6)Подкоренное выражение корня чётной степени должно быть неотрицательным, то есть ≥ 0.
![log_{0,3}(x-2)\geq 0\\\\\left \{ {{x-2}\leq 1 \atop {x-2>0}} \right.\\\\\left \{ {{x\leq 3} \atop {x>2}} \right.\\\\Otvet:\boxed{x\in(2;3]}](https://tex.z-dn.net/?f=log_%7B0%2C3%7D%28x-2%29%5Cgeq%200%5C%5C%5C%5C%5Cleft%20%5C%7B%20%7B%7Bx-2%7D%5Cleq%201%20%5Catop%20%7Bx-2%3E0%7D%7D%20%5Cright.%5C%5C%5C%5C%5Cleft%20%5C%7B%20%7B%7Bx%5Cleq%203%7D%20%5Catop%20%7Bx%3E2%7D%7D%20%5Cright.%5C%5C%5C%5COtvet%3A%5Cboxed%7Bx%5Cin%282%3B3%5D%7D)
4x+y=3 Умножим 1 уравнение на2 8х+2у=6 Прибавим к 1 уравнению 2 уравнение
6x-2y=1 6х-2у=1
14х=7 х=1/2 х=1/2 х=1/2
6х-2у=1 6*(1/2)-2у=1 3-2у=1 у=1 ОТВЕТ (1/2; 1)