Упр.417 ГДЗ Колягин Ткачёва 7 класс (Алгебра)

1) (7x-9)+(2x-8)=1;
2) (12x+5)+(7-3x)=3;
3) (0,2x-7)-(6-0,1x)=2;
4) (1-5,1x)-(1,7x+5,4)=1.
Решить уравнение:
1) (3x-1)^2-(3x-2)^2=0;
2) (y-2)(y+3)-(y-2)^2=5;
3) (x+3)(y+7)-(x+4)^2=0;
4) (y+8)^2-(y+9)(y-5)=117;
5) (3x+2)(3x-2)-(3x-4)^2=28.

1. $$\begin{aligned} (7x-9)+(2x-8)&=1 \\ 7x-9+2x-8&=1 \\ 9x-17&=1 \\ 9x&=18 \\ x&=2 \end{aligned}$$

2. $$\begin{aligned} (12x+5)+(7-3x)&=3 \\ 12x+5+7-3x&=3 \\ 9x+12&=3 \\ 9x&=-9 \\ x&=-1 \end{aligned}$$

3. $$\begin{aligned} (0{,}2x-7)-(6-0{,}1x)&=2 \\ 0{,}2x-7-6+0{,}1x&=2 \\ 0{,}3x-13&=2 \\ 0{,}3x&=15 \\ x&=50 \end{aligned}$$

4. $$\begin{aligned} (1-5{,}1x)-(1{,}7x+5{,}4)&=1 \\ 1-5{,}1x-1{,}7x-5{,}4&=1 \\ -6{,}8x-4{,}4&=1 \\ -6{,}8x&=5{,}4 \\ x&=-\frac{5{,}4}{6{,}8}=-\frac{27}{34} \end{aligned}$$

5. $$\begin{aligned} (3x-1)^2-(3x-2)^2&=0 \\ \bigl((3x-1)-(3x-2)\bigr)\bigl((3x-1)+(3x-2)\bigr)&=0 \\ 1\cdot(6x-3)&=0 \\ 6x-3&=0 \\ x&=\frac12 \end{aligned}$$

6. $$\begin{aligned} (y-2)(y+3)-(y-2)^2&=5 \\ (y-2)\bigl((y+3)-(y-2)\bigr)&=5 \\ (y-2)\cdot 5&=5 \\ y-2&=1 \\ y&=3 \end{aligned}$$

7. $$\begin{aligned} (x+3)(x+7)-(x+4)^2&=0 \\ x^2+10x+21-(x^2+8x+16)&=0 \\ 2x+5&=0 \\ x&=-\frac52 \end{aligned}$$

8. $$\begin{aligned} (y+8)^2-(y+9)(y-5)&=117 \\ y^2+16y+64-(y^2+4y-45)&=117 \\ 12y+109&=117 \\ 12y&=8 \\ y&=\frac23 \end{aligned}$$

9. $$\begin{aligned} (3x+2)(3x-2)-(3x-4)^2&=28 \\ (9x^2-4)-(9x^2-24x+16)&=28 \\ 24x-20&=28 \\ 24x&=48 \\ x&=2 \end{aligned}$$

Ответ

1) $$x=2$$; 2) $$x=-1$$; 3) $$x=50$$; 4) $$x=-\frac{27}{34}$$; 5) $$x=\frac12$$; 6) $$y=3$$; 7) $$x=-\frac52$$; 8) $$y=\frac23$$; 9) $$x=2$$.