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  1. #1
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    Algebra

    If x+y+z=c , show that x^2+y^2+z^2\geq\frac{1}{3}c^2
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  2. #2
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    Quote Originally Posted by thereddevils View Post
    If x+y+z=c , show that x^2+y^2+z^2\geq\frac{1}{3}c^2
    This follows from the Cauchy–Schwarz inequality. Applied to the vectors (x,y,z) and (1,1,1), the C–S inequality says that (x+y+z)^2\leqslant (x^2+y^2+z^2)(1^2+1^2+1^2), or in other words c^2\leqslant3(x^2+y^2+z^2).
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