Ну это же легко!
(Х^2 -2*2х+4)-4+3=0
(Х-2)^2=1.
Х-2=1. Х=3
Х-2= -1. Х=1
(Х^2 -2*3х+9)-9+5=0
(Х-3)^2=4
Х-3=2. Х=5
Х-3= -2. Х=1
(Х^2 +2*4х+16)-16-20=0
(Х+4)^2=36
Х+4=6. Х=2
Х+4= -6. Х= -10
(Х^2 +2*6х+36)-36+32=0
(Х+6)^2 -4=0
(Х+6)^2=4
Х+6=2. Х= -4
Х+6= -2. Х= -8
Задание: <span>Найдите значение выражения
</span>
![\frac{ \frac{y}{5x} - \frac{5x}{y} } {y+5x}](https://tex.z-dn.net/?f=+%5Cfrac%7B+%5Cfrac%7By%7D%7B5x%7D+-+%5Cfrac%7B5x%7D%7By%7D+%7D+%7By%2B5x%7D+)
<span>
х=
![\frac{1}{7}](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B7%7D+)
у=</span>
![\frac{1}{4}](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B4%7D+)
1. Приведем дроби в числителе к общему знаменателю 5xy:
![\frac{y}{5x}](https://tex.z-dn.net/?f=+%5Cfrac%7By%7D%7B5x%7D+)
-
![\frac{5x}{y}](https://tex.z-dn.net/?f=+%5Cfrac%7B5x%7D%7By%7D+)
=
![\frac{5x y^{2} }{5xy}](https://tex.z-dn.net/?f=+%5Cfrac%7B5x+y%5E%7B2%7D+%7D%7B5xy%7D+)
-
![\frac{25 x^{2} y}{5xy}](https://tex.z-dn.net/?f=+%5Cfrac%7B25+x%5E%7B2%7D+y%7D%7B5xy%7D+)
=
![\frac{ y^{2} }{5xy}](https://tex.z-dn.net/?f=+%5Cfrac%7B+y%5E%7B2%7D+%7D%7B5xy%7D)
-
![\frac{25 x^{2} }{5xy}](https://tex.z-dn.net/?f=+%5Cfrac%7B25+x%5E%7B2%7D+%7D%7B5xy%7D+)
=
![\frac{ y^{2}-25 x^{2} }{5xy}](https://tex.z-dn.net/?f=+%5Cfrac%7B+y%5E%7B2%7D-25+x%5E%7B2%7D+%7D%7B5xy%7D+)
2. Разложим числитель: y²-25x²=(y-5x)(y+5x)
3. Подставим:
![\frac{(y-5x)(y+5x)}{5xy}](https://tex.z-dn.net/?f=+%5Cfrac%7B%28y-5x%29%28y%2B5x%29%7D%7B5xy%7D+)
=
![\frac{(y-5x)(y+5x)}{5xy}](https://tex.z-dn.net/?f=+%5Cfrac%7B%28y-5x%29%28y%2B5x%29%7D%7B5xy%7D+)
4.
![\frac{(y-5x)(y+5x)}{5xy}](https://tex.z-dn.net/?f=+%5Cfrac%7B%28y-5x%29%28y%2B5x%29%7D%7B5xy%7D+)
: (y+5x) =
![\frac{(y-5x)(y+5x)}{5xy(y+5x)}](https://tex.z-dn.net/?f=+%5Cfrac%7B%28y-5x%29%28y%2B5x%29%7D%7B5xy%28y%2B5x%29%7D+)
=
![\frac{y-5x}{5xy}](https://tex.z-dn.net/?f=+%5Cfrac%7By-5x%7D%7B5xy%7D+)
5. Подставим числовые значения:
<span>х=
![\frac{1}{7}](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B7%7D+)
у=</span>
Числитель:
y-5x=
![\frac{1}{4}](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B4%7D+)
- 5*
![\frac{1}{7}](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B7%7D+)
=
![\frac{1}{4}](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B4%7D+)
-
![\frac{5}{7}](https://tex.z-dn.net/?f=+%5Cfrac%7B5%7D%7B7%7D+)
=
![\frac{7}{28}](https://tex.z-dn.net/?f=+%5Cfrac%7B7%7D%7B28%7D+)
-
![\frac{20}{28}](https://tex.z-dn.net/?f=+%5Cfrac%7B20%7D%7B28%7D+)
= -
![\frac{13}{28}](https://tex.z-dn.net/?f=+%5Cfrac%7B13%7D%7B28%7D+)
Знаменатель:
5ху=5×
![\frac{1}{4}](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B4%7D+)
×
![\frac{1}{7}](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B7%7D+)
=
(-
![\frac{13}{28}](https://tex.z-dn.net/?f=+%5Cfrac%7B13%7D%7B28%7D+)
):
![\frac{5}{28}](https://tex.z-dn.net/?f=+%5Cfrac%7B5%7D%7B28%7D+)
=
![\frac{(-13)*28}{28*5}](https://tex.z-dn.net/?f=+%5Cfrac%7B%28-13%29%2A28%7D%7B28%2A5%7D+)
=
![\frac{-13*1}{1*5}](https://tex.z-dn.net/?f=+%5Cfrac%7B-13%2A1%7D%7B1%2A5%7D+)
=
![\frac{-13}{5}](https://tex.z-dn.net/?f=+%5Cfrac%7B-13%7D%7B5%7D+)
= - 2
![\frac{3}{5}](https://tex.z-dn.net/?f=+%5Cfrac%7B3%7D%7B5%7D+)
= -2,6
10х - 9=10х+169
10х<span />-10х=169+9
0х= 178
Ответ: решений нет
<span>y=3x² - 6x + 3 и y=[3x-3]</span>
1) если x≥0, то:
3(x²-2x+1)=3(x-1)
3(x-1)²-3(x-1)=0
3(x-1)(x-1-3)=0
3(x-1)(x-4)=0
x₁=1
x₂=4
2) если x<0, то:
3(x²-2x+1)=-3(x-1)
3(x-1)²+3(x-1)=0
3(x-1)(x-1+3)=0
3(x-1)(x+2)=0
x₃=-2
x₄=1 - не подходит условию x<0
Ответ: функции принимают равные значения при x₁=1, x₂=4, x₃=-2