3 [ Completing the square. Sums of squares ]

 Find all real solutions of the equation with 4 unknowns: $x^{2}+y^{2}+z^{2}+t^{2}=x(y+z+t)$.
Move all terms to the left side and represent the expression on the left as the sum of several squares.

## Solution

$1 / 4 x^{2}+(1 / 2 x-y)^{2}+(1 / 2 x-z)^{2}+(1 / 2 x-t)^{2}=0$. From this, it is clear that all terms are equal to zero. We get: $x=1 / 2 x-y=1 / 2 x-z=1 / 2 x-t=0$, which means $x=y=z=t=0$.

## Answer

$(0,0,0,0)$.