Question

[Le Hong Phuc]

Mọi người hãy nêu những bất đẳng thức phụ thường dùng để chứng minh bđt mà mọi người biết?

Answer 1

[o0o I am a studious person o0o(Lê Q...]

I don't now

mik ko biết 

sorry 

......................

Answer 2

[hya_seije_jaumeniz]

1.  \(2ab\le\frac{\left(a+b\right)^2}{2}\le a^2+b^2\) (  \(\forall a;b\))

2.  \(\frac{a}{b}+\frac{b}{a}\ge2\)( \(\forall a;b>0\))

3.  \(\frac{1}{a}+\frac{1}{b}\ge\frac{4}{a+b}\)\(\left(a;b>0\right)\)

4.  \(\frac{1}{ab}\ge\frac{4}{\left(a+b\right)^2}\) \(\left(a;b>0\right)\)

5.  \(\left(a^2+b^2\right)\left(c^2+d^2\right)\ge\left(ac+bd\right)^2\)

6.  \(a^2+b^2+c^2\ge ab+bc+ca\)

7.  \(3\left(a^2+b^2+c^2\right)\ge\left(a+b+c\right)^2\)

8.  \(\left(a+b+c\right)\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\ge9\) \(\left(a;b;c>0\right)\)

9.  \(\frac{a^2}{x}+\frac{b^2}{y}\ge\frac{\left(a+b\right)^2}{x+y}\)\(\left(x;y>0\right)\)

10.  \(\frac{a^2}{x}+\frac{b^2}{y}+\frac{c^2}{z}\ge\frac{\left(a+b+c\right)^2}{x+y+z}\) \(\left(x;y;z>0\right)\)