Question

Tính nhanh:

a) 258² - 242²/254² - 246²

b) 263² + 74. 263 + 37²

c) 136² - 92. 136 + 46²

d) (50² + 48² + ........ + 2²) - (49² + 47² + ......... + 1²)

Answer 1

\(\frac{258^2-242^2}{254^2-246^2}=\frac{\left(258+242\right)\left(258-242\right)}{\left(254+246\right)\left(254-246\right)}=\frac{500.16}{500.8}=2\)

\(263^2+74.263+37^2=263^2+2.37.263+37^2=\left(263+37\right)^2=300^2=90000\)

\(136^2-92.136+46^2=136^2-46.2.136+46^2=\left(136-46\right)^2=90^2=8100\)

\(=\left(50^2-49^2\right)+\left(48^2-47^2\right)+.....+\left(2^2-1^2\right)=\left(50+49\right)\left(50-49\right)+\left(48+47\right)\left(48-47\right)+....+\left(2+1\right)\left(2-1\right)=\left(50+49+....+1\right)=\frac{51.50}{2}=51.25=1275\)