Question

用配方法说明无论x为何实数,代数式2x^2-20x+51的值恒大于0

Answer 1

原式=2(x^2-10x)+51=2(x^2-10x+25-25)+51=2(x-5)^2-2*25+51=2(x-5)^2+1恒大于0

Answer 2

2x^2-20x+51
=2（x^2-10x+25）+1
=2(x-5)^2+1

因为2(x-5)^2≥0恒成立
所以2(x-5)^2+1＞0恒成立

还请给个满意答案，谢谢