Question

a) Calculati (x-1)^2 -x^2 -(x+1)^2 + (x+2)^2
b) Folosind observatiile de la punctul a), calculaţi:
90^2-91^2-92^2+93^2+900^2-901^2-902^2+903^2​

Answer 1

(x - 1)² - x² - (x + 1)² + (x + 2)² =

= x² - 2x + 1 - x² - x² - 2x - 1 + x² + 4x + 4

= x² - x² - x² + x² - 2x - 2x + 4x + 4

reducem

= 4

90² - 91² - 92² + 93² + 900² - 901² - 902² + 903² =

= ​ (90² - 91²) + (93² - 92²) + (900² - 901²) + (903² - 902²

folosim a² - b² = (a - 1)(a + 1)

= (90 - 91)(90 + 91) + (93 - 92)(93 + 92) + (900 - 901)(900 + 901) + (903 - 902)(903 + 902)

= - 1×181 + 1×185 - 1×1801 + 1×1805

= 1805 - 1801 + 185 - 181

= 4 + 4

= 8