求行列式A=
|α2(α+1)2(α+2)2(α+3)2|
|b2(b+1)2(b+2)2(b+3)2|
|c2(c+1)2(c+2)2(c+3)2|
|d2(d+1)2(d+2)2(d+3)2|
【正确答案】：A= |α2 α2+2α+1 α2+4α+4 α2+6α+9| |b2 b2+2b+1 b2+4b+4 b2+6b+9| |c2 c2+2c+1 c2+4c+4 c2+6c+9| |d2 d2+2d+1 d2+4d+4 d2+6d+9| = |α2 2α+1 4α+4 6α+9| |b2 2b+1 4b+4 6b+9| |c2 2c+1 4c+4 6c+9| |d2 2d+1 4d+4 6d+9| = |α 2α+1 2 6| |b 2b+1 2 6| |c 2c+1 2 6| |d 2d+1 2 6| =0
