证明代数式5x^2-6x+11的值恒大于0

问题描述:

证明代数式5x^2-6x+11的值恒大于0

原式=5(x²-6x/5)+11
=5(x²-6x/5+9/25-9/25)+11
=5(x²-6x/5+9/25)-9/5+11
=5(x-3/5)²+46/5
5(x-3/5) ² ≥0
所以5(x-3/5)²+46/5>0
所以值恒大于0