Question

Tính nhanh:
a) 127² + 146.127 + 72²

b) 9⁸.2⁸ - (18⁴ - 1)(18⁴ + 1)

c) 20² + 18² + 16² + .... + 4² + 2² - (19² + 17² + .... + 3² + 1)

Answer 1

Giải:

a) Sửa đề: 127² + 146.127 + 73²

\(127^2+146.127+73^2=\left(127+7\right)^2=200^2=40000\)

b) \(9^8.2^8-\left(18^4-1\right)\left(18^4+1\right)=18^8-\left(18^4-1\right)^2=18^8-18^8-1=-1\)

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

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

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

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

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

Chúc bạn học tốt!