\(x\left(x-y+z\right)=-11;y\left(y-x-z\right)=25;z\left(z+x-y\right)=35\)
Suy ra \(x\left(x-y+z\right)+y\left(y-z-x\right)+z\left(z+x-y\right)=49\)
\(\Leftrightarrow x\left(x-y+z\right)-y\left(x-y+z\right)+z\left(x-y+z\right)=49\)
\(\Leftrightarrow\left(x-y+z\right)\left(x-y+z\right)=49\)
\(\Leftrightarrow\left(x-y+z\right)^2=49\)
Do đó, \(x-y+z=\pm7\)
Suy ra.....
x(x−y+z)=−11;y(y−x−z)=25;z(z+x−y)=35x(x−y+z)=−11;y(y−x−z)=25;z(z+x−y)=35
Suy ra x(x−y+z)+y(y−z−x)+z(z+x−y)=49x(x−y+z)+y(y−z−x)+z(z+x−y)=49
⇔x(x−y+z)−y(x−y+z)+z(x−y+z)=49⇔x(x−y+z)−y(x−y+z)+z(x−y+z)=49
⇔(x−y+z)(x−y+z)=49⇔(x−y+z)(x−y+z)=49
⇔(x−y+z)2=49⇔(x−y+z)2=49
Do đó, x−y+z=±7x−y+z=±7
Suy ra thay vào x(x-y+z) ta sẽ tìm được các số trên .
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