比较大小2a^4-a^2与2a^3-1

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比较大小2a^4-a^2与2a^3-1
比较大小2a^4-a^2与2a^3-1

比较大小2a^4-a^2与2a^3-1
A = 2a^4 - a^2
B = 2a^3 - 1
A - B
= 2a^4 - 2a^3 - a^2 + 1
= 2a^3(a - 1) - (a^2 - 1)
= (2a^3 - a - 1)(a - 1)
= (2a^2 + 2a + 1)(a - 1)^2
2a^3 - a - 1
= (a - 1)(2a^2 + 2a + 1)
其中:2a^2 + 2a + 1 > 0
所以:
a = 1 .A = B
a ≠1 .A > B

^ 这个符号 ^ 是 什么意思

A = 2a^4 - a^2
B = 2a^3 - 1
A - B
= 2a^4 - 2a^3 - a^2 + 1
= 2a^3(a - 1) - (a^2 - 1)
= (2a^3 - a - 1)(a - 1)
= (2a^2 + 2a + 1)(a - 1)^2
2a^3 - a - 1
= (a - 1)(2a^2 + 2a + 1)
2a^2+2a+1=a^2+(a^2+2a+1)
=a^2+(a+1)^2恒大于0
而又有(a-1)^2恒大于0
所以有A恒大于B

a = 1 .............. A = B
a ≠1 .............. A > B