Упр.17.20 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) (x-12)(x+12)=2(x-6)^2-x^2;
2) (3x-1)^2+(4x+2)^2=(5x-1)(5x+1);
3) (6x-1)^2-(3-8x)(3+8x)=(10x+1)^2;
4) 5(x+2)^2+(2x-1)^2-9(x+3)(x-3)=22.

1. $$ (x-12)(x+12)=2(x-6)^2-x^2 $$

   $$ x^2-144=2(x^2-12x+36)-x^2 $$

   $$ x^2-144=2x^2-24x+72-x^2 $$

   $$ x^2-144=x^2-24x+72 $$

   $$ -144=-24x+72 $$

   $$ -216=-24x $$

   $$ x=9 $$

2. $$ (3x-1)^2+(4x+2)^2=(5x-1)(5x+1) $$

   $$ 9x^2-6x+1+16x^2+16x+4=25x^2-1 $$

   $$ 25x^2+10x+5=25x^2-1 $$

   $$ 10x=-6 $$

   $$ x=-\frac{3}{5} $$

3. $$ (6x-1)^2-(3-8x)(3+8x)=(10x+1)^2 $$

   $$ 36x^2-12x+1-(9-64x^2)=100x^2+20x+1 $$

   $$ 36x^2-12x+1-9+64x^2=100x^2+20x+1 $$

   $$ 100x^2-12x-8=100x^2+20x+1 $$

   $$ -32x=9 $$

   $$ x=-\frac{9}{32} $$

4. $$ 5(x+2)^2+(2x-1)^2-9(x+3)(x-3)=22 $$

   $$ 5(x^2+4x+4)+(4x^2-4x+1)-9(x^2-9)=22 $$

   $$ 5x^2+20x+20+4x^2-4x+1-9x^2+81=22 $$

   $$ 16x+102=22 $$

   $$ 16x=-80 $$

   $$ x=-5 $$

Ответ

1) $$x=9$$; 2) $$x=-\frac{3}{5}$$; 3) $$x=-\frac{9}{32}$$; 4) $$x=-5$$.