Номер 14 гдз 8 класс алгебра Муравин Муравина

Номер 14

 

1) 592
592 = (60 - 1)2 =
= 3600 - 120 + 1 = 3481;
2) 622
(60 + 2)2 =
= 3600 + 240 + 4 = 3844;
3) 313
(30 + 1)3 =
= 27000 + 2700 + 90 + 1 =
= 29791;
4) 393
(40 - 1)3 =
= 64000 - 4800 + 120 - 1 =
= 59319;
5) 2562 - 442
(256 + 44)(256 - 44) =
= 300 • 212 = 63600; 
6) 43 • 57
(50 - 7)(50 + 7) =
= 502 - 72 = 2500 - 49 =
= 2451; \begin{equation} 7)\frac{181^{2}-71^{2}}{312^{2}-202^{2}} \end{equation} \begin{equation} \frac{(181+71)(181-71)}{(312+202)(312-202)}= \end{equation} \begin{equation} =\frac{252\cdot 110}{514\cdot 110}= \end{equation} \begin{equation} =\frac{126\cdot 2}{257\cdot 2}=\frac{126}{257}. \end{equation} 8) 203 • 197 - 201 • 199
(200 + 3)(200 - 3) -
- (200 + 1)(200 - 1) =
= 2002 - 32 - (2002 - 12) =
= 2002 - 9 - 2002 + 1 = -8.