Question

1.Tính nhanh:  \(\frac{2004^3+1}{2004^2-2003}\);   \(\frac{2004^3-1}{2004^2+2005}\)

2. Cho a+b+c+d=0. CMR:

a³+b³+c³+d³=3(ac-bd)(b+d)

 

Answer 1

Bạn sửa lại đề bài câu 2) nhé ^^

2) \(a+b+c+d=0\Leftrightarrow a+b=-c-d\Leftrightarrow\left(a+b\right)^3=-\left(c+d\right)^3\)

\(\Leftrightarrow a^3+b^3+3ab\left(a+b\right)=-\left[c^3+d^3+3cd\left(c+d\right)\right]\)

\(\Leftrightarrow a^3+b^3+c^3+d^3=-3cd\left(c+d\right)-3ab\left(a+b\right)\)

\(\Leftrightarrow a^3+b^3+c^3+d^3=3ab\left(c+d\right)-3cd\left(c+d\right)\)

\(\Leftrightarrow a^3+b^3+c^3+d^3=3\left(c+d\right)\left(ab-cd\right)\)

Answer 2

đề đúng ak bạn