用配方法证明—10x^+7x—4的值恒小于0。

2024-12-12 20:19:34
推荐回答(3个)
回答1:

-10x²+7x-4
=-10(x²-7/10x)-4
=-10(x²-7/10+49/400)-4+10×49/400
=-10(x-7/20)²-111/40≤111/40<0
恒小于0,得证

回答2:

一10x^2+7x一4=一10(x^2一7x/10)一4
=一10(x一7/20)^2一4+49/40
=一10(x一7/20)^2一111/40
故原式恒小于0。

回答3:

证明:-10^2+7x-4=-10(x^2-7/10x+(7/20)^2-(7/20)^2)-4=-10(x-7/20)^2+7/20-4=-10(x-7/20)^2-73/20<0