Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
đổi ẩn
\(\left(a;b;c\right)=\left(\frac{1}{x};\frac{1}{y};z\right)\)\(\Rightarrow\)\(x+y+z=3\)
\(P=\Sigma\frac{1}{\sqrt{xy+x+y}}\ge\Sigma\frac{2\sqrt{3}}{xy+x+y+3}\ge\frac{18\sqrt{3}}{\frac{\left(x+y+z\right)^2}{3}+2\left(x+y+z\right)+9}=\sqrt{3}\)
dấuu "=" xảy ra khi \(a=b=c=1\)
Áp dụng bđt bu nhi a, ta có \(M^2\le3\left(\frac{a}{b+c+2a}+...\right)\)
mà \(\frac{a}{b+c+2a}\le\frac{1}{4}\left(\frac{a}{a+b}+\frac{a}{a+c}\right)\)
tương tự, ta có \(M^2\le\frac{3}{4}\left(\frac{a}{a+b}+\frac{a}{a+c}+\frac{b}{a+b}+\frac{b}{b+c}+\frac{c}{a+c}+\frac{c}{c+b}\right)=\frac{9}{4}\)
=>\(M\le\frac{3}{2}\)
dấu = xảy ra <=> a=b=c
Bài 4 nha
Áp dụng BĐT cô si ta có
\(\frac{1}{x^2}+x+x\ge3\sqrt[3]{\frac{1}{x^2}.x.x}=3.\)
Tương tự với y . \(A\ge6\)dấu = xảy ra khi x=y=1
\(\left(\frac{x^2+3x}{x^3+3x^2+9x+27}+\frac{3}{x^2+9}\right):\left(\frac{1}{x-3}-\frac{6x}{x^3-3x^2+9x-27}\right)\)
\(=\left(\frac{x\left(x+3\right)}{\left(x+3\right)\left(x^2+9\right)}+\frac{3}{x^2+9}\right):\left(\frac{1}{x-3}-\frac{6x}{\left(x-3\right)\left(x^2+9\right)}\right)\)
\(=\left(\frac{x}{x^2+9}+\frac{3}{x^2+9}\right):\left(\frac{x^2+9-6x}{\left(x-3\right)\left(x^2+9\right)}\right)=\frac{x+3}{x^2+9}:\frac{x^2+9-6x}{\left(x-3\right)\left(x^2+9\right)}\)
\(=\frac{\left(x+3\right)\left(x-3\right)\left(x^2+9\right)}{\left(x^2+9\right)\left(x^2-6x+9\right)}=\frac{\left(x+3\right)\left(x-3\right)}{\left(x-3\right)\left(x-3\right)}=\frac{x+3}{x-3}\)
b) \(Voix>0\Rightarrow P\ne\varnothing\)(mk ko chac)
c) \(P\inℤ\Leftrightarrow x+3⋮x-3\Leftrightarrow x-3\in\left\{-1;-2;-3;-6;1;2;3;6\right\}\)
sau do tinh
cau nay la toan lp 8 nha
\(\text{Σ}\frac{a}{b+2c+3d}=\text{Σ}\frac{a^2}{ab+2ac+3ad}\ge\frac{\left(a+b+c+d\right)^2}{6\left(ab+bc+cd+ad\right)}\)
\(=\frac{\left(a+b\right)^2+\left(c+d\right)^2+2\left(a+b\right)\left(c+d\right)}{6\left(ab+bc+cd+ad\right)}=\frac{a^2+c^2+b^2+d^2+2ab+2cd+2\left(a+b\right)\left(c+d\right)}{6\left(ab+bc+cd+ad\right)}\)
\(\ge\frac{4\left(ab+bc+cd+ad\right)}{6\left(ab+bc+cd+ad\right)}=\frac{2}{3}\)
Dấu = xảy ra khi a=b=c=d
Áp dụng BĐT Cauchy-Schwarz ta có:
\(\frac{a}{b+2c+3d}+\frac{b}{c+2d+3a}+\frac{c}{d+2a+3b}+\frac{d}{a+2b+3c}\)
\(=\frac{a^2}{ab+2ac+3ad}+\frac{b^2}{bc+2bd+3ab}+\frac{c^2}{cd+2ac+3bc}+\frac{d^2}{ad+2bd+3cd}\)
\(\ge\frac{\left(a+b+c+d\right)^2}{4.\left(ab+ad+bc+bd+ca+cd\right)}\)\(\ge\frac{\left(a+b+c+d\right)^2}{\frac{3}{2}.\left(a+b+c+d\right)^2}=\frac{2}{3}\)
Dấu "=" xảy ra \(\Leftrightarrow a=b=c=d\)
๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ ๑๑۩۞۩๑๑ v
Bài này chịu mất.Cần có nhiều thời gian suy nghĩ