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关于不等式的证明方法较多,这在很多书刊中都作过较详细的讨论。本文就用判别式来证明不等式探求几种思考方法,供大家在教学时参考。第一种方法:一元二次方程ax~2+bx+c=0(a≠0)有实根的充要条件是判别式△≥0。用这个结论来证明不等式,其关键是根据已知条件来构造一个实系数二次方程,再利用二次方程有实根的条件判别式△≥0推出所要证的不等式。例1 已知x、y、z是实数,且满足等式
There are many ways to prove inequality, which has been discussed in more detail in many publications. This article uses the discriminant to prove inequality to explore several ways of thinking for everyone in the teaching reference. The first method: the necessary and sufficient condition for the real root of the one-dimensional quadratic equation ax~2+bx+c=0(a≠0) is that the discriminant Δ≥0. Using this conclusion to prove the inequality, the key is to construct a real coefficient quadratic equation according to the known conditions, and then use the conditional discriminant △ ≥ 0 of the quadratic equation with real roots to derive the inequality to be proved. Example 1 It is known that x, y, and z are real numbers and satisfy the equation