Question

8 arată că următoarele numere sunt pătrate perfecte a 303 ori 200 plus 303 ori 100 plus 303 ori 3 b 1254 la puterea a doua minus 1254 minus 1253 c 2132 la puterea a doua minus 2132 minus 2131​

Answer 1

a.

$303 \times 200 + 303 \times 100 + 303 \times 3 = \\ 303 \times (200 + 100 + 3) = \\ 303 \times 303 = \\ = {303}^{2}$

b.

${1254}^{2} - 1254 - 1253 = \\ 1254 \times (1254 - 1) - 1253 = \\ 1254 \times 1253 - 1253 = \\ 1253 \times (1254 - 1) = \\ 1253 \times 1253 = \\ = {1253}^{2}$

c.

${2132}^{2} - 2132 - 2131 = \\ 2132 \times (2132 - 1) - 2131 = \\ 2132 \times 2131 - 2131 = \\ 2131 \times (2132 - 1) = \\ 2131 \times 2131= \\ = {2131}^{2}$

Answer 2

$\it a)\ 303\cdot200+303\cdot100+303\cdot3=303\cdot(200+100+3)=303\cdot303=303^2\\ \\ b)\ 1254^2-1254-1253=1254^2-1254-1254+1=1254(1254-1-1)+1=\\ \\ =1254\cdot12542+1=(1253+1)(1253-1)+1=1253^2-1+1=1253^2$