论文部分内容阅读
判别式定理在初中数学中的应用很广泛,一些几何问题可以通过构造一元二次方程,利用判别式的性质来解决。本文举数例说明。 例1 矩形ABCD中,AB=5,AD=8,在AB、AD上各取点Q、P,使PQ=3.求五边形PQBCO面积的最小值。解:设AP=x,AQ=y,△APQ的面积为S,x/y=t∵PQ=3,∴x~2+y~2=9.则S=1/2xy=去分母,得2st-9t+2s=0,∵t为实数,∴△=81-16s~2≥0,解得S≤9/4. ∴五边形PQBCD面积的最小值是5×8-9/4=151/4.
The discriminant theorem is widely used in junior high school mathematics. Some geometric problems can be solved by constructing a quadratic equation with the use of discriminant properties. This article gives a few examples. Example 1 In rectangular ABCD, AB=5 and AD=8. Take points Q and P on AB and AD to make PQ=3. Find the pentagon PQBCO area minimum value. Solution: Let AP = x, AQ = y, △ APQ area is S, x / y = t ∵ PQ = 3, ∴ x ~ 2+ y ~ 2 = 9. Then S = 1/2xy = denominator, 2st-9t+2s=0, ∵t is a real number, ∴△=81-16s~2≥0, and the solution is S≤9/4. The minimum value of the PQBCD area of the pentagon is 5×8-9/4= 151/4.