用比较法证明不等式:2a4-a2>=2a3-1急求
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用比较法证明不等式:2a4-a2>=2a3-1急求
用比较法证明不等式:2a4-a2>=2a3-1急求
用比较法证明不等式:2a4-a2>=2a3-1急求
做差得
2a4-a2-(2a3-1)
=2a^3(a-1)-(a^2-1)
=2a^3(a-1)-(a-1)(a+1)
=(a-1)(2a^3-a-1)
=(a-1)(a-1)(2a^2+2a+1)
=(a-1)^2(2a^2+2a+1)
由于(a-1)^2≥0
2a^2+2a+1>0 (其判别式小于0)
所以上式≥0
即2a4-a2>=2a3-1