Question

Tính nhanh 
a,\(A=100^2-99^2+98^2-97^2+...+2^2-1^2\)
b,\(B=\left(20^2+18^2+...+2^2\right)-\left(19^2+17^2+....+3^2+1^2\right)\)
c,\(C=\frac{780^2-220^2}{125^2+150.125+75^2}\)
d,\(D=2.\left(a+5\right).\left(a+4\right)-\left(a+5\right)^2-\left(a^2-9a-17\right)\)với a=99

Answer 1

a/ A = 100² - 99² + 98² -...+2² - 1²

= (100² - 99²) + (98² - 97²) +...+ (2² - 1²)

= 199 + 195 + 191 + ... + 1

= (\(\frac{199-1}{4}+1\))(\(\frac{199+1}{2}\)) = 5050

Answer 2

b/ Y chang câu a luôn nha

c/ \(C=\frac{780^2-220^2}{125^2+150.125+75^2}=\frac{\left(780-220\right)\left(780+220\right)}{\left(125+75\right)^2}\)

\(=\frac{560.1000}{200^2}=14\)

Answer 3

d/ 2(a + 4)(a + 5) - (a + 5)² - (a² - 9a - 17) 

= 17a + 32 = 17(a + 1) + 15 = 1700 + 15 = 1715