\(A=\dfrac{2}{1+a+a^2}=\dfrac{2}{a^2+a+\dfrac{1}{4}+\dfrac{3}{4}}\)
\(=\dfrac{2}{\left(a+\dfrac{1}{2}\right)^2+\dfrac{3}{4}}\le\dfrac{8}{3}\)
Khi \(a=-\dfrac{1}{2}\)
Cho a,b,c > 0 và 15(\(\dfrac{1}{a^2}\)+\(\dfrac{1}{b^2}\)+\(\dfrac{1}{c^2}\))=3+\(\dfrac{1}{a}\)+\(\dfrac{1}{b}\)+\(\dfrac{1}{c}\).
Tìm max P=\(\dfrac{1}{\sqrt{5a^2+2ab+2b^2}}\)+\(\dfrac{1}{\sqrt{5b^2+2bc+2c^2}}\)+\(\dfrac{1}{\sqrt{5c^2+2ca+2a^2}}\)
Cho P=\(\left(\dfrac{\sqrt{x}-2}{x-1}-\dfrac{\sqrt{x}+2}{x+2\sqrt{x}+1}\right).\left(\dfrac{1-\sqrt{x}}{\sqrt{2}}\right)^2\)
a) Tìm ĐKXĐ
b) Rút gọn P
c) Tìm x để P>0
d) Tìm P max
Bài 1: Cho x,y,z >0 thỏa mãn:
xy+yz+xz \(\ge\)2xyz
Tìm Max A= (x-1)(y-1)(z-1)
Bài 2: Cho a,b,c >0 thỏa mãn:
\(\dfrac{c+1}{c+3}\ge\dfrac{1}{a+2}+\dfrac{3}{b+4}\)
Tìm Min M= (a+1)(b+1)(c+1)
1. cho P = \(\left(\dfrac{1}{\sqrt{a}-1}-\dfrac{2\sqrt{a}}{a-1}+\dfrac{\sqrt{a}}{a+1}\right):\dfrac{\sqrt{a}}{\sqrt{a}+1}\)
a. Rút gọn P
b. Tìm a để P < \(\dfrac{1}{2}\)
p=\(\left(\dfrac{1}{\sqrt{\left\{x\right\}}-3}-\dfrac{1}{\sqrt{\left\{x\right\}}+3}\right):\dfrac{3}{\sqrt{\left\{x\right\}}-3}\)
a, tìm x để p max . tìm max
Cho a,b,c >0 thỏa a+b+c \(\ge9\)
Tìm Min:
\(P=2\sqrt{a^2+\dfrac{b^2}{3}+\dfrac{c^2}{5}}+\sqrt{\dfrac{1}{a}+\dfrac{9}{b}+\dfrac{25}{c}}\)
1. So sánh: \(\sqrt{3}\) và \(5-\sqrt{8}\)
2. Tìm Min, Max
a/ x = \(\sqrt{x^2-2x+5}\)
b/ y = \(\sqrt{\dfrac{x^2}{4}-\dfrac{x}{6}+1}\)
cho a,b,c dương khác nhau đôi một thỏa \(\left\{{}\begin{matrix}ab+bc=2c^2\\2a\le c\end{matrix}\right.\)
tìm Max \(\dfrac{a}{a-b}+\dfrac{b}{b-c}+\dfrac{c}{c-a}\)
cho a,b,c thỏa \(\left\{{}\begin{matrix}1\le a\\b,c\le3\\a+b+c=8\end{matrix}\right.\)
tìm MAX MIN \(\dfrac{1}{4a+b+c}+\dfrac{1}{a+4b+c}+\dfrac{1}{a+b+4c}\)
