Question

Cho biết \(1^2+2^2+3^2+...+10^2=385\).Tính nhanh : \(\left(12^2+14^2+16^2+18^2+20^2\right)-\left(1^2+3^2+5^5+7^2+9^2\right)\)

Answer 1

\(A=\left(12^2+14^2+16^2+18^2+20^2\right)-\left(1^2+3^2+5^2+7^2+9^2\right)\)

\(A=\left(12^2-1^2\right)+\left(14^2-3^2\right)+\left(16^2-5^2\right)+\left(18^2-7^2\right)+\left(20^2-9^2\right)\)\(A=\left(12+1\right)\left(12-1\right)+\left(14+3\right)\left(14-3\right)+\left(16-5\right)\left(16+5\right)+\left(18-7\right)\left(18+7\right)+\left(20-9\right)\left(20+9\right)\)

\(A=11.13+11.17+11.21+11.25+11.29\)

\(A=11.\left(13+17+21+25+29\right)\)

\(A=11.\left[\left(13+17\right)+\left(21+29\right)+25\right]\)

\(A=11.\left(30+50+25\right)\)

\(A=11.105=1155\)