Question

tính biểu thức sau bằng cách nhanh nhất : 

 

(10²+8²+6²+4²+2²) - (9²+7²+5²+3²+1²)

Answer 1

= \(10^2+8^2+6^2+4^2+2^2-9^2-7^2-5^2-3^2-1\)-1

=\(55\)

Answer 2

\(\left(10^2+8^2+6^2+4^2+2^2\right)-\left(9^2+7^2+5^2+3^2+1^2\right)\)

\(=10^2+8^2+6^2+4^2+2^2-9^2-7^2-5^2-3^2-1^2\)

\(=\left(10^2-9^2\right)+\left(8^2-7^2\right)+...+\left(2^2-1^2\right)\)

\(=\left(10-9\right)\left(10+9\right)+\left(8-7\right)\left(8+7\right)+...+\left(2-1\right)\left(1+2\right)\)

\(=10+9+8+7+...+2+1\)

\(=\frac{\left(1+10\right)\cdot10}{2}\)

\(=55\)