When I tried to prove the triangle inequality $|z_1+z_2| \leq |z_1| + |z_2|$ algebraically for complex variables $z_1$ and $z_2$, I came across this inequality and found that this is always true no matter what. Can anyone explain why?
2026-04-24 22:52:08.1777071128
Why does $2x_1x_2y_1y_2 \leq x_1^2y_2^2+x_2^2y_1^2$?
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Hint
Develop $(x_1y_2-x_2y_1)^2\ge0$.