Упр.33.18 ГДЗ Мордкович 7 класс (Алгебра)

б) (-7*2/7)2;
в) (7*3/14)2;
г) (-13*3/13)2.

1. $$\left(12\frac{1}{12}\right)^2=\left(12+\frac{1}{12}\right)^2$$
   $$=12^2+2\cdot 12\cdot \frac{1}{12}+\left(\frac{1}{12}\right)^2$$
   $$=144+2+\frac{1}{144}=146\frac{1}{144}$$
2. $$\left(-7\frac{2}{7}\right)^2=\left(-7-\frac{2}{7}\right)^2$$
   $$=(-7)^2+2\cdot 7\cdot \frac{2}{7}+\left(\frac{2}{7}\right)^2$$
   $$=49+4+\frac{4}{49}=53\frac{4}{49}$$
3. $$\left(7\frac{3}{14}\right)^2=\left(7+\frac{3}{14}\right)^2$$
   $$=7^2+2\cdot 7\cdot \frac{3}{14}+\left(\frac{3}{14}\right)^2$$
   $$=49+3+\frac{9}{196}=52\frac{9}{196}$$
4. $$\left(-13\frac{3}{13}\right)^2=\left(-13-\frac{3}{13}\right)^2$$
   $$=(-13)^2+2\cdot 13\cdot \frac{3}{13}+\left(\frac{3}{13}\right)^2$$
   $$=169+6+\frac{9}{169}=175\frac{9}{169}$$

Ответ

а) $$146\frac{1}{144}$$; б) $$53\frac{4}{49}$$; в) $$52\frac{9}{196}$$; г) $$175\frac{9}{169}$$.