Задание 8 Параграф 15 ГДЗ Рабочая тетрадь 1 Мерзляк Полонский 7 класс (Алгебра)

1) (7x-1)^2-36=0;
2) (5x+2)^2-16x^2=0;
3) (3y-1)^2-(y+3)^2=0;
4) 64(4y+1)^2-(12y-5)^2=0.

1. $$ (7x-1)^2-36=0 $$
   $$ (7x-1)^2-6^2=0 $$
   $$ (7x-1-6)(7x-1+6)=0 $$
   $$ (7x-7)(7x+5)=0 $$
   $$ 7x-7=0 \quad \text{или} \quad 7x+5=0 $$
   $$ x=1 \quad \text{или} \quad x=-\frac{5}{7} $$
2. $$ (5x+2)^2-16x^2=0 $$
   $$ (5x+2)^2-(4x)^2=0 $$
   $$ (5x+2-4x)(5x+2+4x)=0 $$
   $$ (x+2)(9x+2)=0 $$
   $$ x+2=0 \quad \text{или} \quad 9x+2=0 $$
   $$ x=-2 \quad \text{или} \quad x=-\frac{2}{9} $$
3. $$ (3y-1)^2-(y+3)^2=0 $$
   $$ (3y-1-(y+3))(3y-1+(y+3))=0 $$
   $$ (2y-4)(4y+2)=0 $$
   $$ 2y-4=0 \quad \text{или} \quad 4y+2=0 $$
   $$ y=2 \quad \text{или} \quad y=-\frac{1}{2} $$
4. $$ 64(4y+1)^2-(12y-5)^2=0 $$
   $$ \bigl(8(4y+1)-(12y-5)\bigr)\bigl(8(4y+1)+(12y-5)\bigr)=0 $$
   $$ (32y+8-12y+5)(32y+8+12y-5)=0 $$
   $$ (20y+13)(44y+3)=0 $$
   $$ 20y+13=0 \quad \text{или} \quad 44y+3=0 $$
   $$ y=-\frac{13}{20} \quad \text{или} \quad y=-\frac{3}{44} $$

Ответ

1) $$x=1,\; x=-\frac{5}{7}$$; 2) $$x=-2,\; x=-\frac{2}{9}$$; 3) $$y=2,\; y=-\frac{1}{2}$$; 4) $$y=-\frac{13}{20},\; y=-\frac{3}{44}$$.