已知方程X²-ax+2a=0的两个实数分别是x1,x2.则(X1-X2)²-X1X2的最小值为?
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![已知方程X²-ax+2a=0的两个实数分别是x1,x2.则(X1-X2)²-X1X2的最小值为?](/uploads/image/z/3708292-4-2.jpg?t=%E5%B7%B2%E7%9F%A5%E6%96%B9%E7%A8%8BX%26%23178%3B-ax%2B2a%3D0%E7%9A%84%E4%B8%A4%E4%B8%AA%E5%AE%9E%E6%95%B0%E5%88%86%E5%88%AB%E6%98%AFx1%2Cx2.%E5%88%99%28X1-X2%29%26%23178%3B-X1X2%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%E4%B8%BA%3F)
已知方程X²-ax+2a=0的两个实数分别是x1,x2.则(X1-X2)²-X1X2的最小值为?
已知方程X²-ax+2a=0的两个实数分别是x1,x2.则(X1-X2)²-X1X2的最小值为?
已知方程X²-ax+2a=0的两个实数分别是x1,x2.则(X1-X2)²-X1X2的最小值为?
x² - ax + 2a = 0
x1 + x2 = - (- a)/1 = a
x1 * x2 = (2a)/1 = 2a
(x1 - x2)² - x1x2
= (x1)² + (x2)² - 2(x1x2) - x1x2
= (x1)² + 2(x1x2) + (x2)² - 5(x1x2)
= (x1 + x2)² - 5(x1x2)
= a² - 5(2a)
= a² - 10a + 5² - 5²
= (a - 5)² - 25
∴最小值是- 25