Упр.17.21 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

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

1. $$\begin{aligned} (3x+2)^2+(4x-1)(4x+1)&=(5x-1)^2 \\ 9x^2+12x+4+16x^2-1&=25x^2-10x+1 \\ 25x^2+12x+3&=25x^2-10x+1 \\ 12x+3&=-10x+1 \\ 22x&=-2 \\ x&=-\frac{1}{11} \end{aligned}$$

2. $$\begin{aligned} (4x+1)^2-(1-3x)(1+3x)&=(5x+2)^2 \\ 16x^2+8x+1-(1-9x^2)&=25x^2+20x+4 \\ 16x^2+8x+1-1+9x^2&=25x^2+20x+4 \\ 25x^2+8x&=25x^2+20x+4 \\ -12x&=4 \\ x&=-\frac{1}{3} \end{aligned}$$

3. $$\begin{aligned} 2(m+1)^2+3(m-1)^2-5(m+1)(m-1)&=-4 \\ 2(m^2+2m+1)+3(m^2-2m+1)-5(m^2-1)&=-4 \\ 2m^2+4m+2+3m^2-6m+3-5m^2+5&=-4 \\ -2m+10&=-4 \\ -2m&=-14 \\ m&=7 \end{aligned}$$

Ответ

1) $$x=-\frac{1}{11}$$; 2) $$x=-\frac{1}{3}$$; 3) $$m=7$$.