Question

tÍNH NHANH:

a, A=\(85^2+170.15+225\)

b, B=\(20^2-19^2+18^2-17^2+...............+2^2-1^2\)

Answer 1

a)\(A=85^2+170.15+225\)
\(=85^2+2.85.15+15^2\)
\(=\left(85+15\right)^2\)
\(=100^2=10000\)
b)\(B=20^2-19^2+18^2-17^2+...+2^2-1^2\)

\(=\left(20^2+18^2+16^2+...+4^2+2^2\right)-\left(19^2+17^2+15^2+...+3^2+1^2\right)\)

\(=20^2 +18^2+16^2+...+4^2+2^2-19^2-17^2-15^2-...-3^2-1^2\)

\(=\text{(20 + 19).(20 - 19) + (18 + 17).(18 - 17) + (16 + 15).(16 - 15) + .... + (2 + 1).(2 - 1)}\)

\(=\text{20 + 19 + 18 + 17 + 16 + ..... + 2 + 1}\)

\(=\frac{20\left(20+1\right)}{2}=210\)