When I give you the answer to prove Cauchy inequality, to construct a quadratic function, there must be 2n numbers b 1b2b3. . Bn and a 1a2a3. . . An, the constructor f(x) 1=a 1 square x square+2a1b1x+b1square, and f(x)2=a2 square x square +2a2b2x+b2 square, so that. . . +An Dang) X Dang +2(a 1b 1+a2b2+. . . +anbn)x+(b 1 square +b2 square+. . . +bn), because f(x) is equal to or greater than 0, delta is equal to or less than 0, so (a 1b 1+a2b2+). . . +anbn) square < =(a 1 square +a2 square+. . . +An Dang) (b 1 Dang +b2 Party+. . . +bn squared), Cauchy inequality proof.

For mathematical construction method, it is very common in high school. Cauchy inequality cannot be used directly. Some big questions often say, as shown in the constructor, you will find that the constructed function is very similar to the known function. Constructors are often used to prove inequalities.

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