一元二次方程的公式法是指使用一元二次方程的求根公式来解方程。一元二次方程的一般形式是 ax2 + bx + c = 0,其中 a ≠ 0。求根公式为:
x = (-b ± √(b2 4ac)) / (2a)
以下是一些一元二次方程公式法的练习题:
1. 解方程:x2 5x + 6 = 0
2. 解方程:2x2 4x 6 = 0
3. 解方程:x2 + 2x 3 = 0
4. 解方程:3x2 6x + 2 = 0
5. 解方程:x2 10x + 25 = 0
接下来,我将给出这些方程的解答:
1. 解方程:x2 5x + 6 = 0
根据公式法,a = 1, b = -5, c = 6
x = (-(-5) ± √((-5)2 416)) / (21)
x = (5 ± √(25 24)) / 2
x = (5 ± √1) / 2
x = (5 ± 1) / 2
x1 = (5 + 1) / 2 = 6 / 2 = 3
x2 = (5 1) / 2 = 4 / 2 = 2
解得:x1 = 3, x2 = 2
2. 解方程:2x2 4x 6 = 0
根据公式法,a = 2, b = -4, c = -6
x = (-(-4) ± √((-4)2 42(-6))) / (22)
x = (4 ± √(16 + 48)) / 4
x = (4 ± √64) / 4
x = (4 ± 8) / 4
x1 = (4 + 8) / 4 = 12 / 4 = 3
x2 = (4 8) / 4 = -4 / 4 = -1
解得:x1 = 3, x2 = -1
3. 解方程:x2 + 2x 3 = 0
根据公式法,a = 1, b = 2, c = -3
x = (-2 ± √(22 41(-3))) / (21)
x = (-2 ± √(4 + 12)) / 2
x = (-2 ± √16) / 2
x = (-2 ± 4) / 2
x1 = (-2 + 4) / 2 = 2 / 2 = 1
x2 = (-2 4) / 2 = -6 / 2 = -3
解得:x1 = 1, x2 = -3
4. 解方程:3x2 6x + 2 = 0
根据公式法,a = 3, b = -6, c = 2
x = (-(-6) ± √((-6)2 432)) / (23)
x = (6 ± √(36 24)) / 6
x = (6 ± √12) / 6
x = (6 ± 2√3) / 6
x1 = (6 + 2√3) / 6 = (3 + √3) / 3
x2 = (6 2√3) / 6 = (3 √3) / 3
解得:x1 = (3 + √3) / 3, x2 = (3 √3) / 3
5. 解方程:x2 10x + 25 = 0
根据公式法,a = 1, b = -10, c = 25
x = (-(-10) ± √((-10)2 4125)) / (21)
x = (10 ± √(100 100)) / 2
x = (10 ± √0) / 2
x = (10 ± 0) / 2
x1 = x2 = 10 / 2 = 5
解得:x1 = x2 = 5
以上是这些方程的解答过程。