tìm GTNN

K

khuongchinh

lam cach chia nhu tren mo mit lam em ak, anh lam the nay
P=(x*x+x)^2 + 2(x*x+x)+1
dat t=x*x+x (t>= -1/4)
P=t*t+2t+1 (nho la t>= -1/4)
P>=9/16
sor, anh chua pit viet cong thuc mong la em hiu
 
P

pemi_thefame

[TEX]A = x^4 + 2x^3 + 3x^2 + 2x +1 = (x^2 + x + 1)^2[/TEX] (tự phân tích thành nhân tử nhé)
[TEX]= [(x^2 + x + \frac{1}{4}) + \frac{3}{4}]^2 = [(x + \frac{1}{2})^2] + \frac{3}{4}]^2 (x + \frac{1}{2})^2\geq0\Rightarrow (x + \frac{1}{2})^2] + \frac{3}{4}\geq\frac{3}{4}\Rightarrow A\geq\frac{9}{16} \Rightarrow Amin = \frac{9}{16} khi x = -\frac{1}{2}[/TEX]
 
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