MathIsEverything
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- Joined
- Sep 17, 2022
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- 14
Prove, that for any real numbers x, y, z satisfying the equality
[math]x^2 + y^2 + z^2 = 1[/math]the ineaquality
[math]|x+y+z| + |x+y-z| + |x-y+z| + |-x+y+z| ≥ 2\sqrt2[/math]is true
[math]x^2 + y^2 + z^2 = 1[/math]the ineaquality
[math]|x+y+z| + |x+y-z| + |x-y+z| + |-x+y+z| ≥ 2\sqrt2[/math]is true