Question

数学问题

若M=10a²+2b²-7a+6，N=a²+2b²+5a+1，试比较M和N的大小

Answer 1

M-N=10a²+2b²-7a+6-(a²+2b²+5a+1)
=9a²-12a+5
=9(a-2/3)²+1
≥1
则M>N

Answer 2

M-N=10a²+2b²-7a+6-(a²+2b²+5a+1)
=9a²-12a+5
=9(a-2/3)²+1
≥1
所以，M>N

Answer 3

M-N=9a^2-12a+5=(3a-2)^2+1≥1
所以M>N

Answer 4

M-N=9a²-12a+5=9a²-12a+4+1，配方可得M-N=(3a-2)²+1＞0，则有M＞N恒成立

Answer 5

相减 M-N=9a^2-12a^2+5
△=12^2-4*9*5=-36<0
所以M>N

Answer 6

M-N=9a²-12a+5，判别式小于0，所以M>N