Упр.7.98 ГДЗ Дорофеев Суворова 7 класс (Алгебра)

б) 2(у — 1) — (1 — у)2 = 0;
в) 3(х — 2) + (х2 — 4) = 0;
г) (у — 3)2 — 4(3 — у) = 0.

1. $$3x(x-1)+(x^2-1)=0$$

   $$3x(x-1)+(x-1)(x+1)=0$$

   $$ (x-1)(3x+x+1)=0 $$

   $$ (x-1)(4x+1)=0 $$

   $$ x-1=0 \quad \text{или} \quad 4x+1=0 $$

   $$ x=1 \quad \text{или} \quad x=-\frac14 $$

2. $$2(y-1)-(1-y)^2=0$$

   $$2(y-1)-(y-1)^2=0$$

   $$ (y-1)\bigl(2-(y-1)\bigr)=0 $$

   $$ (y-1)(3-y)=0 $$

   $$ y-1=0 \quad \text{или} \quad 3-y=0 $$

   $$ y=1 \quad \text{или} \quad y=3 $$

3. $$3(x-2)+(x^2-4)=0$$

   $$3(x-2)+(x-2)(x+2)=0$$

   $$ (x-2)(3+x+2)=0 $$

   $$ (x-2)(x+5)=0 $$

   $$ x-2=0 \quad \text{или} \quad x+5=0 $$

   $$ x=2 \quad \text{или} \quad x=-5 $$

4. $$ (y-3)^2-4(3-y)=0 $$

   $$ (3-y)^2-4(3-y)=0 $$

   $$ (3-y)\bigl((3-y)-4\bigr)=0 $$

   $$ (3-y)(-1-y)=0 $$

   $$ 3-y=0 \quad \text{или} \quad -1-y=0 $$

   $$ y=3 \quad \text{или} \quad y=-1 $$

Ответ

а) $$x=1,\; x=-\frac14$$; б) $$y=1,\; y=3$$; в) $$x=2,\; x=-5$$; г) $$y=-1,\; y=3$$.