ta có : \(\left(a+b\right)^3+\left(a-b\right)^3-2a^3\)
\(=\left(a+b+a-b\right)\left(\left(a+b\right)^2+\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\right)-2a^3\)
\(=\left(2a\right)\left(a^2+2ab+b^2+a^2-b^2+a^2-2ab+b^2\right)-2a^3\)
\(\)\(=2a\left(3a^2+b^2\right)-2a^3=6a^3+2ab^2-2a^3=4a^3+2ab^2\)
Cho a,b cùng dấu. Chứng minh:
\(\dfrac{a^2b}{2a^2+b^3}+\dfrac{2}{3}\ge\dfrac{a^2+2ab}{2a^2+b^2}\)
Cho \(a,b,c>0\) thỏa mãn \(ab+bc+ca=3\) . CMR : \(\sqrt[3]{\dfrac{a}{b\left(b+2c\right)}}+\sqrt[3]{\dfrac{b}{c\left(c+2a\right)}}+\sqrt[3]{\dfrac{c}{a\left(a+2b\right)}\ge\dfrac{3}{\sqrt[3]{3}}}\)
Bài 1: Cho a,b,c là những số dương thỏa mãn: a+b+c=3
CMR: \(\dfrac{a^2}{a+2b^3}+\dfrac{b^2}{b+2c^3}+\dfrac{c^2}{c+2a^3}\ge1\)
Bài 2: Cho a, b, c thỏa mãn: ab+bc+ca=3
CMR: \(\dfrac{a}{2b^3+1}+\dfrac{b}{2c^3+1}+\dfrac{c}{2a^3+1}\ge1\)
Bài 3: Cho a, b, c > 0. CMR: \(\dfrac{a^2}{b}+\dfrac{b^2}{c}+\dfrac{c^2}{a}\ge a+3b\)
Dấu = xảy ra khi a=b=2c
Cho a,b,c,d > 0. Chứng minh \(\frac{a^4}{a^3+2b^3}+\frac{b^4}{b^3+2c^3}+\frac{c^4}{c^3+2d^3}+\frac{d^4}{d^3+2a^3}\) ≥ \(\frac{a+b+c+d}{3}\)
Cho a, b, c, d > 0. CMR: \(\frac{a^4}{a^3+2b^3}+\frac{b^4}{b^3+2c^3}+\frac{c^4}{c^3+2d^3}+\frac{d^4}{d^3+2a^3}\ge\frac{a+b+c+d}{3}\) (Dùng Cô-si )
Biết\(\frac{a+2}{3}+\frac{2a-7}{3}=b\). Tính a-b ???
khai triển hằng đẳng thức:
a)x2 + x +1/2
b)(3x +y). (y-3x)
c) (x+2y-3)2+2(3-x)(x+2y - 3) +(3-x)2
d) (a-b)2 -4(c-3b +2a)(a-b) + (c-3b +2a)2
cho a>b,chứng minh
a)2a+3>2b+1
b)-2a-6<-2b
giá trị của a-b biết \(\dfrac{a+2}{3}+\dfrac{2a-7}{3}=b\)
