Question 5
Suppose \(x,y,z,t\) are real numbers such that
\[|x+y+z-t|\le1,\quad |y+z+t-x|\le1,\quad |z+t+x-y|\le1,\quad |t+x+y-z|\le1.\]
Prove that \(x^2+y^2+z^2+t^2\le1\).
\[|x+y+z-t|\le1,\quad |y+z+t-x|\le1,\quad |z+t+x-y|\le1,\quad |t+x+y-z|\le1.\]
Prove that \(x^2+y^2+z^2+t^2\le1\).