Question

Câu 4: Tìm x; y; z thỏa mãn phương trình sau:

x²- 10x + y² - 6y + 27 + z² = 2z - 8

Answer 1

PT <=> \(x^2-10x+y^2-6y+z^2-2z+35=0\)

<=> \(\left(x^2-10x+25\right)+\left(y^2-6y+9\right)+\left(z^2-2z+1\right)=0\)

<=> \(\left(x-5\right)^2+\left(y-3\right)^2+\left(z-1\right)^2=0\)

Mà \(\left(x-5\right)^2;\left(y-3\right)^2;\left(z-1\right)^2\ge0\)

<=> \(\left\{{}\begin{matrix}x-5=0\\y-3=0\\z-1=0\end{matrix}\right.< =>\left\{{}\begin{matrix}x=5\\y=3\\z=1\end{matrix}\right.\)