<span>а) 5х² - 3= х² - 3
</span> 5х² - х²-<span>3+3= 0
4х</span>²=0
х=0
<span>б) х² + 15х = 8х
х</span>²+15х-8х=0
х²+7х=0
х*(х+7)=0
х₁=0 х+7=0
х₂=-7
в) <span>х (х-2) = -х²
х</span>²-2х+х²=0
2х²-2х=0
2х*(х-1)=0
2х=0 ⇒ х₁=0
х-1=0 ⇒х₂=1
40:7,50=5.33333333
ответ; 5 сырков
<span>y=x-ex ну веть понятно всё!</span>
Для начала упростим правую часть
![2\log_2(x^2-8x+6) \geq 2\log_24+\log_2(2x-1) \\ \log_2(x^2-8x+6)^2 \geq \log_2(16(2x-1))](https://tex.z-dn.net/?f=2%5Clog_2%28x%5E2-8x%2B6%29%20%5Cgeq%202%5Clog_24%2B%5Clog_2%282x-1%29%20%20%5C%5C%20%5Clog_2%28x%5E2-8x%2B6%29%5E2%20%5Cgeq%20%5Clog_2%2816%282x-1%29%29)
ОДЗ:
![\left \{ {{x^2-8x+6>0} \atop {2x-1>0}} \right.](https://tex.z-dn.net/?f=%20%5Cleft%20%5C%7B%20%7B%7Bx%5E2-8x%2B6%3E0%7D%20%5Catop%20%7B2x-1%3E0%7D%7D%20%5Cright.%20)
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![2x-1>0 \\ x> \frac{1}{2}](https://tex.z-dn.net/?f=2x-1%3E0%20%5C%5C%20x%3E%20%5Cfrac%7B1%7D%7B2%7D%20)
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![x^2-8x+6>0](https://tex.z-dn.net/?f=x%5E2-8x%2B6%3E0)
Приравниваем к нулю
![x^2-8x+6=0 \\ \\ D=b^2-4ac=64-24=40; \sqrt{D} =2 \sqrt{10} \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\boxed{x_1_,_2= \frac{-b \pm \sqrt{D} }{2a} } \\ x_1_,_2=4\pm \sqrt{10}](https://tex.z-dn.net/?f=x%5E2-8x%2B6%3D0%20%5C%5C%20%20%5C%5C%20D%3Db%5E2-4ac%3D64-24%3D40%3B%20%5Csqrt%7BD%7D%20%3D2%20%5Csqrt%7B10%7D%20%20%5C%5C%20%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5Cboxed%7Bx_1_%2C_2%3D%20%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%7BD%7D%20%7D%7B2a%7D%20%7D%20%5C%5C%20x_1_%2C_2%3D4%5Cpm%20%5Csqrt%7B10%7D%20)
___+__(4-√10)____-__(4+√10)___+___
<u />
![x \in (-\infty;4-\sqrt{10})\cup (4+\sqrt{10};+\infty)](https://tex.z-dn.net/?f=x%20%5Cin%20%28-%5Cinfty%3B4-%5Csqrt%7B10%7D%29%5Ccup%20%284%2B%5Csqrt%7B10%7D%3B%2B%5Cinfty%29)
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ОДЗ:
![x \in ( \frac{1}{2} ;4-\sqrt{10})\cup (4+\sqrt{10};+\infty)](https://tex.z-dn.net/?f=x%20%5Cin%20%28%20%5Cfrac%7B1%7D%7B2%7D%20%3B4-%5Csqrt%7B10%7D%29%5Ccup%20%284%2B%5Csqrt%7B10%7D%3B%2B%5Cinfty%29)
![(x^2-8x+6)^2 \geq 16(2x-1) \\ (x^2-8x+6)^2-16(2x-1) \geq 0](https://tex.z-dn.net/?f=%28x%5E2-8x%2B6%29%5E2%20%5Cgeq%2016%282x-1%29%20%5C%5C%20%28x%5E2-8x%2B6%29%5E2-16%282x-1%29%20%5Cgeq%200)
Приравниваем к нулю
![(x^2-8x+6)^2-16(2x-1)=0 \\ x^4-16x^3+76x^2-96x+36-32x+16=0 \\ x^4-16x^3+76x^2-128x+52=0](https://tex.z-dn.net/?f=%28x%5E2-8x%2B6%29%5E2-16%282x-1%29%3D0%20%5C%5C%20x%5E4-16x%5E3%2B76x%5E2-96x%2B36-32x%2B16%3D0%20%5C%5C%20x%5E4-16x%5E3%2B76x%5E2-128x%2B52%3D0)
Разложим одночлены в сумму нескольких
![x^4-12x^3-4x^3+26x^2+48x^2+2x^2-104x-24x+52=0 \\](https://tex.z-dn.net/?f=x%5E4-12x%5E3-4x%5E3%2B26x%5E2%2B48x%5E2%2B2x%5E2-104x-24x%2B52%3D0%20%5C%5C%20)
Сделаем группировку
![(x^4-12x^3+26x^2) - (4x^3-48x^2+104x) + (2x^2-24x+52)=0](https://tex.z-dn.net/?f=%28x%5E4-12x%5E3%2B26x%5E2%29%20-%20%284x%5E3-48x%5E2%2B104x%29%20%2B%20%282x%5E2-24x%2B52%29%3D0)
Выносим общий множитель
![x^2(x^2-12x+26)-4x(x^2-12x+26)+2(x^2-12x+26)=0 \\ (x^2-12x+26)(x^2-4x+2)=0](https://tex.z-dn.net/?f=x%5E2%28x%5E2-12x%2B26%29-4x%28x%5E2-12x%2B26%29%2B2%28x%5E2-12x%2B26%29%3D0%20%5C%5C%20%28x%5E2-12x%2B26%29%28x%5E2-4x%2B2%29%3D0)
Имеем 2 квадратные уравнения
![x^2-12x+26=0 \\ D=40 \\ x_1_,_2=6 \pm \sqrt{10} \\ \\ x^2-4x+2=0 \\ D=b^2-4ac=(-4)^2-8=8 \\ x_3_,_4=2\pm\sqrt{2}](https://tex.z-dn.net/?f=x%5E2-12x%2B26%3D0%20%5C%5C%20D%3D40%20%5C%5C%20x_1_%2C_2%3D6%20%5Cpm%20%5Csqrt%7B10%7D%20%5C%5C%20%20%5C%5C%20x%5E2-4x%2B2%3D0%20%5C%5C%20D%3Db%5E2-4ac%3D%28-4%29%5E2-8%3D8%20%5C%5C%20x_3_%2C_4%3D2%5Cpm%5Csqrt%7B2%7D)
Находим решение неравенства:
_+__(2-√2)___-_(6-√10)_+__(2+√2)__-__(6+√10)___+__
![x \in (-\infty;2-\sqrt{2}]\cup[6-\sqrt{10};2+ \sqrt{2} ]\cup[6+\sqrt{10};+\infty)](https://tex.z-dn.net/?f=x%20%5Cin%20%28-%5Cinfty%3B2-%5Csqrt%7B2%7D%5D%5Ccup%5B6-%5Csqrt%7B10%7D%3B2%2B%20%5Csqrt%7B2%7D%20%5D%5Ccup%5B6%2B%5Csqrt%7B10%7D%3B%2B%5Cinfty%29)
С учетом ОДЗ решение неравенства будет иметь
![x \in (0.5;2- \sqrt{2} ]\cup [6+\sqrt{10};+\infty)](https://tex.z-dn.net/?f=x%20%5Cin%20%280.5%3B2-%20%5Csqrt%7B2%7D%20%5D%5Ccup%20%5B6%2B%5Csqrt%7B10%7D%3B%2B%5Cinfty%29)
Ответ:
![x \in (0.5;2- \sqrt{2} ]\cup [6+\sqrt{10};+\infty)](https://tex.z-dn.net/?f=x%20%5Cin%20%280.5%3B2-%20%5Csqrt%7B2%7D%20%5D%5Ccup%20%5B6%2B%5Csqrt%7B10%7D%3B%2B%5Cinfty%29)