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Với điều kiện đã cho thì không tìm được $x,y,z$ cụ thể bạn nhé.
![](https://rs.olm.vn/images/avt/0.png?1311)
x2-6x+y2+10y+34=-(4z-1)2
=>x2-6x+9+y2+10y+25+(4z-1)2=0=B
=>(x-3)2+(y+5)2+(4z-1)2=0
với mọi x,y,z ta có :
(x-3)2>=0
(y+5)2>=0
(4z-1)2>=0
=>(x-3)2+(y+5)2+(4z-1)2>=0
hay B>=0
dấu bằng xảy ra khi (x-3)2=0 => x-3=0 =>x=3
=>(y+5)2=0 =>y+5=0 =>y=-5
=>(4z-1)2=0 =>4z-1=0 => z=1/4
Vậy y=-5
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x^2-6x+y^2+10y+34=-\left(4z-1\right)^2\)
\(\Leftrightarrow\left(x^2-6x+9\right)+\left(y^2+10y+34\right)+\left(4z-1\right)^2=0\)
\(\Leftrightarrow\left(x-3\right)^2+\left(y+5\right)^2+\left(4z-1\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(x-3\right)^2=0\\\left(y+5\right)^2=0\\\left(4z-1\right)^2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=-5\\z=\dfrac{1}{4}\end{matrix}\right.\)
Vậy........
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x^2-6x+y^2+10y+34=-\left(4z-1\right)^2\)
\(x^2-6x+9+y^2+10y+25+\left(4z-1\right)^2=0\)
\(\left(x-3\right)^2+\left(y+5\right)^2+\left(4z-1\right)^2=0\)
\(\left[\begin{array}{nghiempt}x-3=0\\y+5=0\\4z-1=0\end{array}\right.\)
\(\left[\begin{array}{nghiempt}x=3\\y=-5\\z=\frac{1}{4}\end{array}\right.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x^2-6x+y^2+10y+34=-(4z-1)^2 \\\Leftrightarrow (x^2-6x+9)+(y^2+10y+25)+(4z-1)^2=0 \\\Leftrightarrow (x-3)^2+(y+5)^2+(4z-1)^2=0\)
Ta có:
\((x-3)^2\geq 0 \ \forall \ x;(y+5)^2\geq 0 \ \forall \ y;(4z-1)^2\geq 0 \ \forall \ z \\\Rightarrow (x-3)^2+(y+5)^2+(4z-1)^2\geq 0\)
Dấu '=' xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}x-3=0\\y+5=0\\4z-1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=-5\\z=\dfrac{1}{4}\end{matrix}\right.\)
Vậy giá trị của y thỏa mãn là -5
x2−6x+y2+10y+34=−(4z−1)2
x^2-6x+9+y^2+10y+25+(4z-1)^2=0x2−6x+9+y2+10y+25+(4z−1)2=0
(x-3)^2+(y+5)^2+(4z-1)^2=0(x−3)2+(y+5)2+(4z−1)2=0
{nghiempt}x-3=0\\y+5=0\\4z-1=0
{nghiempt}x=3\\y=-5\\z={1}{4}