Question

求证:(x^2-4)(x-3)(x-7)+100的值为非负数

Answer 1

(x^2 - 4) (x - 3) (x - 7) + 100;

(-3 + x) (-2 + x) (-7 + x) (2 + x) + 100;

(6 - 5 x + x^2) (-14 - 5 x + x^2) + 100;

设 - 5 x + x^2 = y

(6 + y) (-14 + y) + 100;

-84 - 8 y + y^2 + 100;

16 - 8 y + y^2;

(-4 + y)^2 >= 0