Question

Tính nhanh giá trị các biểu thức sau

a. A=85^2+170*15+225

b.B=20^2-19^2+18^2-17^2+.....+2^2-1^2

Answer 1

Answer 2

b, B=20²-19²+18²-17²+...+2²-1²

=(20²-19²)+(18²-17²)+...+(2²-1²)

= (20-19)(20+19)+(18-17)(18+17)+..+(2-1)(2+1)

=39+35+...+3

=\(\xrightarrow[10sốhạng]{3+..+35+39}\)

=\(\frac{\left(39+3\right).10}{2}=210\)

Vậy B =210

Answer 3

bạn nhớ tick cho mk nhé

Answer 4

a) \(A=85^2+2\cdot85\cdot15+15^2\)

\(A=\left(85+15\right)^2=100^2=10000\)

b) \(B=\left(20-19\right)\left(20+19\right)+\left(18-17\right)\left(18+17\right)+...+\left(2+1\right)\left(2-1\right)\)\(B=39+35+...+3\)

\(=\frac{\left(39+3\right)\left[\left(39-3\right):4+1\right]}{2}\)

\(=\frac{42\cdot10}{2}=210\)