Tìm x, y, z ∈ Z⁺

\(x^3+y^3+z^3=\left(x+y+z\right)^2\)

Giải phương trình nghiệm nguyên:

a) \(2x+2y+xy=x^2+y^2\)

b) \(x^5-y^4=4\)

c) \(x^3+y^2-x+3y=2021\)

Bài 1: Gpt

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

b) \(\sqrt[3]{2x^3+6}=\sqrt{x^2-3x+3}-x\)

c) \(x^2-3x+4=3\sqrt{x^3-6x^2+11x-6}\)

Bài 2: Giải hệ:

\(\left\{{}\begin{matrix}\left(x-1\right)^3+y^2=\sqrt[3]{x\left(2x+1\right)}\\3x^2-x+\dfrac{1}{2}=y\sqrt{x^2+x}\end{matrix}\right.\)

Bài 1: Gpt

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

b) \(\sqrt[3]{2x^3+6}=\sqrt{x^2-3x+3}-x\)

c) \(x^2-3x+4=3\sqrt{x^3-6x^2+11x-6}\)

Bài 2: Giải hệ:

\(\left\{{}\begin{matrix}\left(x-1\right)^3+y^2=\sqrt[3]{x\left(2x+1\right)}\\3x^2-x+\dfrac{1}{2}=y\sqrt{x^2+x}\end{matrix}\right.\)

Gpt

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

b) \(\sqrt[3]{2x^3+6}=\sqrt{x^2-3x+3}-x\)

Cho x,y,z là độ dài 3 cạnh 1 tam giác.

Tìm max \(A=\sqrt{1-\dfrac{x}{y+z}}+\sqrt{1-\dfrac{y}{z+x}}+\sqrt{1-\dfrac{z}{x+y}}\)

 Cho a,b,c>0 tm: abc=1

CM: \(a+b+c\ge\dfrac{ab+1}{b+1}+\dfrac{bc+1}{c+1}+\dfrac{ca+1}{a+1}\)