-2<=x<=5

=>(x+2)(x-5)<=0

=>\(x^2-3x-10\le0\)

=>\(x^2\le3x+10\) (1)

-2<=y<=5

=>(y+2)(y-5)<=0

=>\(y^2-3y-10\le0\)

=>\(y^2\le3y+10\)

=>\(2y^2\le6y+20\) (2)

-2<=z<=5

=>(z+2)(z-5)<=0

=>\(z^2-3z-10\le0\)

=>\(z^2\le3z+10\)

=>\(3z^2\le9z+30\) (3)

Từ (1),(2),(3) suy ra M<=3x+10+6y+20+9z+30=3(x+2y+3z)+60=3*9+60=87

Dấu '=' xảy ra khi (x;y;z)∈{(-2;-2;5);(5;5;-2)}

\(\Leftrightarrow\left(x^2+y^2+1-2xy+2x-2y\right)+\left(y^2-4y+4\right)=4\)

\(\Leftrightarrow\left(x-y+1\right)^2+\left(y-2\right)^2=4=2^2+0^2=0^2+2^2\)

\(\Rightarrow x;y\)

\(\frac{2}{x+y+z}=\frac{x}{2y+2z+1}=\frac{y}{2x+2z+1}=\frac{z}{2x+2y-2}=\frac{x+y+z}{4\left(x+y+z\right)}=\frac{1}{4}\)

\(\Rightarrow\hept{\begin{cases}2y+2z+1=4x\\2x+2z+1=4y\\x+y+z=8\end{cases}}\Leftrightarrow\hept{\begin{cases}x=y=\frac{17}{6}\\z=\frac{7}{3}\end{cases}}\)

1D  2C

Câu 1: D

Câu 2: C

\(37xy=x^2+y^2+5x^2y^2+60\ge2xy+5x^2y^2+60\)

\(\Rightarrow5x^2y^2-35xy+60\le0\)

\(\Rightarrow5\left(xy-3\right)\left(xy-4\right)\le0\)

\(\Rightarrow\left[{}\begin{matrix}xy=3\\xy=4\end{matrix}\right.\) 

Thế vào pt đầu \(\Rightarrow...\)

a) \(\dfrac{x}{2}=\dfrac{y}{3}\Rightarrow\left(\dfrac{x}{2}\right)^2=\left(\dfrac{y}{3}\right)^2=\dfrac{x.y}{2.3}=\dfrac{54}{6}=9\)

\(\Rightarrow\left\{{}\begin{matrix}x^2=36\\y^2=81\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}x=\pm6\\y=\pm9\end{matrix}\right.\)

b) \(\dfrac{x}{5}=\dfrac{y}{3}\Rightarrow\left(\dfrac{x}{5}\right)^2=\left(\dfrac{y}{3}\right)^2=\dfrac{x^2-y^2}{5^2-3^2}=\dfrac{4}{16}=\dfrac{1}{4}\)

\(\Rightarrow\left\{{}\begin{matrix}x^2=\dfrac{25}{4}\\y^2=\dfrac{9}{4}\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=\pm\dfrac{5}{2}\\y=\pm\dfrac{3}{2}\end{matrix}\right.\)

c: Ta có: \(\dfrac{x}{2}=\dfrac{y}{3}\)

nên \(\dfrac{x}{10}=\dfrac{y}{15}\)

Ta có: \(\dfrac{y}{5}=\dfrac{z}{7}\)

nên \(\dfrac{y}{15}=\dfrac{z}{21}\)

mà \(\dfrac{x}{10}=\dfrac{y}{15}\)

nên \(\dfrac{x}{10}=\dfrac{y}{15}=\dfrac{z}{21}\)

Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:

\(\dfrac{x}{10}=\dfrac{y}{15}=\dfrac{z}{21}=\dfrac{92}{46}=2\)

Do đó: x=20; y=30; z=42