Give \(a;b;c\ge-1\) và \(a^2+b^2+c^2=9\).

Find Min \(M=a^3+b^3+c^3\)

Give: a;b;c>0 and \(a^2+b^2+c^2=1\). Prove that:

    \(\dfrac{1}{3-ab}+\dfrac{1}{3-bc}+\dfrac{1}{3-ca}\le\dfrac{3}{2}\)

x²+x+1=0

\(\Leftrightarrow\left(x^2+x+\dfrac{1}{4}\right)+\dfrac{3}{4}=0\)

\(\Leftrightarrow\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}=0\)

\(\Rightarrow x\in\varnothing\)

\(\Rightarrow A=x^n+\dfrac{1}{x^n}\in\varnothing\)

\(2x^2+2y^2-4x+2y-17\)

\(=\left(2x^2-4x+2\right)+\left(2y^2+2y\right)-19\)

\(=2\left(x-1\right)^2+2\left(y^2+y\right)-19\)    \(\left(1\right)\)

Thay x=3;y=-2 ta có:

\(\left(1\right)=2\left(3-1\right)^2+2\left(2^2-2\right)-19\)

\(=2.2^2+2.2-19\)

\(=8+4-19\)

\(=-7\)

\(\Delta ABC\) \(has\)\(AB\perp AC\)\(and\)\(AB< AC;BC^2=4.AB.AC\). Find the value of \(\widehat{B}\)and\(\widehat{C}\)

1+2+3+...+10=?

Solve these equations:

a) \(\dfrac{6}{\left(x+1\right)\left(x+2\right)}+\dfrac{8}{\left(x-1\right)\left(x+4\right)}=1\)

b)\(\dfrac{x^2-3x+5}{x^2-4x+5}+\dfrac{x^2-5x+5}{x^2-6x+5}=\dfrac{-1}{4}\)

Give: \(a+b+c=4\).Prove:

\(\sqrt{a+b}+\sqrt{b+c}+\sqrt{c+a}>4\)

\(C=\dfrac{3\left|x\right|+2}{4\left|x\right|-5}\)         \(\left(x\in Z\right)\)

a)Find Max,Min C

b) Find x when \(C\in N\)

Solve the equation:

\(x.\dfrac{8-x}{x-1}\left(x-\dfrac{8-x}{x-1}\right)=15\)

Prove: \(\dfrac{a+b}{bc+a^2}+\dfrac{b+c}{ca+b^2}+\dfrac{c+a}{ab+c^2}\le\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\)

\(\left(a;b;c>0\right)\)