Question

[Quỳnh Như]

Tính nhanh giá trị của các biểu thức sau:

a) \(A=85^2+75^2+65^2+55^2-45^2-35^2-25^2-15^2\)

b) \(B=1^2-2^2+3^2-4^2+5^2-6^2+...+2011^2-2012^2\)

c) \(C=\dfrac{1}{1975}\left(\dfrac{2}{1945}-1\right)-\dfrac{1}{1945}\left(1-\dfrac{2}{1975}\right)-\dfrac{1974}{1975}.\dfrac{1946}{1945}-\dfrac{3}{1975.1945}\)

d) \(D=\left(2^9+2^7+1\right)\left(2^{23}-2^{21}+2^{19}-2^{17}+2^{14}-2^{10}+2^9-2^7+1\right)\)

Answer 1

[Rimuru tempest]

a) \(A=85^2-45^2+75^2-35^2+65^2-25^2+55^2-15^2\)

\(A=\left(85-45\right)\left(85+45\right)+....+\left(55-15\right)\left(55+15\right)\)

\(A=40.130+40.110+40.90+40.70\)

\(A=40.\left(130+110+90+70\right)=40.400=16000\)

Answer 2

[Rimuru tempest]

b) \(B=\left(1-2\right)\left(1+2\right)+\left(3-4\right)\left(3+4\right)+...+\left(2011-2012\right)\left(2011+2012\right)\)

\(B=-3-7-11-...-4023\)

\(B=-\left(3+7+11+...+4023\right)\)

\(B=-\dfrac{\left(3+4023\right)\left[\dfrac{\left(4023-3\right)}{4}+1\right]}{2}=2025078\)