中四既一元二次方程-急

2010-09-21 6:50 am

解下列各方程。(答案需以最簡根式表示。)
1)
(2x+3)^2=72

2)
8-3x^2+6x=0

3)
2x^2-7=2x

4)
5x^2=10x+7

5)
4x^2-5=6x

答案係x=.......
急急急.唔識做~~~
萬分感激!!!!!

回答 (1)

[匿名]

2010-09-21 7:44 am

✔ 最佳答案

Question 1
(2x+3)^2=72
x = (±√72 - 3 )/ 2
=- 3/2 ±3√2

Question 2
8-3x^2+6x=0
3x^2 - 6x = 8
(x^2 - 2x) = 8/3
(x - 1)^2 = 8/3 + 1^2
x = 1 ±√11/3

Question 3
2x^2 - 7 = 2x
2x^2 - 2x = 7
x^2 - x = 7/2
(x - 1/2)^2 = 7/2 + (1/2)^2
x = 1/2 ±√15/4
x = (1 ±√15)/2

Question 4
5x^2 = 10x + 7
5x^2 - 10x = 7
x^2 - 2x = 7/5
(x - 1)^2 = 7/5 + 1^2
x = 1 ±√12/5
x = 1 ±2√3/5

Question 5
4x^2 - 5 = 6x
4x^2 - 6x = 5
x^2 - 3/2x = 5/4
(x - 3/4)^2 = 5/4 + (3/4)^2
x = 3/4 ±√29/16
x = (3 ±√29)/4

2010-09-20 23:44:56 補充：
All done by completing square method.

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