一元二次方程

1.
(2p + 7)(p - 3) = 2p
2p² - 6p + 7p - 21 = 2p
2p² - p - 21 = 0
(2p - 7)(p + 3) = 0
p = 7/2 or p = -3

2.
(a + 1)(4a - 5) = 3a - 2
4a² - 5a + 4a - 5 = 3a - 2
4a² - 4a - 3 = 0
(2a + 1)(2a - 3) = 0
a = -1/2 or a = 3/2

3.
(x - 2)² = 36
(x - 2)² - 6² = 0
(x - 2 + 6)(x - 2 - 6) = 0
(x + 4)(x - 8) = 0
x = -4 or x = 8

4.
(a + 2/5)² = 64
a + 2/5 = ±8
a = 8 - 2/5 or a = -8 - 2/5
a = 38/5 or a = -42/5

5.
(x + 2)² = 5
x + 2 = ±√5
x = -2 ± √5

6.
3x² - 9x + 4 = 0
x = { -(-9) ± √[(-9)² - 4(3)(4)] } / (2 × 3)
x = (9 ± √33)/6

7.
(x - 3)(x + 4) = 2
x² + 4x - 3x - 12 = 2
x² + x - 14 = 0
x² + x = 14
x² + 2x(1/2) + (1/2)² = 14 + (1/2)²
(x + 1/2)² = 14 + 1/4
(x + 1/2)² = 57/4
x + 1/2 = ±√(57/4)
x + 1/2 = ±√57 / 2
x = (-1 ± √57)/2

8.
2x² - 4x - 1 = 0
2x² - 4x = 1
2x² - 4x + 2 = 1 + 2
2(x² - 2x + 1) = 3
2(x - 1)² = 3
(x - 1)² = 3/2
x - 1 = ±√(3/2)
x = 1 ± √(3/2)


2015-01-04 21:09:42 補充：
以上的所有答案除了計算之外，其實我是有幫你用電腦核對過的。

最後一題如果你希望 rationalize 分母，你可以考慮：

x = 1 ± √(3/2)
= 1 ± √3/√2
= 1 ± √6/2

1,(2p+7)(p-3)=2p
(2p*p)+(2p*-3)+(7*p)+(7*-3)=2p
2p^2-6p+7p-21=2p
2p^2-21=p
2p^2-p-21=0
(2p-7)(p+3)=0
p=7/2 or p=-3

2,(a+1)(4a-5)=3a-2
4a^2-5a+4a-5=3a-2
4a^2-4a-3=0
(2a+1)(2a-3)=0
a=-1/2 or a=3/2

3,(x-2)^2=36
(x-2)=+-6
x=6+2 or x=-6+2
x=8 or x=-4

4,(a+2/5)^2=64
(a+2/5)=+-64
a=64-2/5 or a=-64-2/5
a=63.6 or a=-64.4

5,(x+2)^2=5
x^2+4x+4=5
x^2+4x-1=0
x=-4+-開方(4^2-4*1*-1)/2
x=-4+-開方(20)/2

6,3x^2-9x+4=0
x=-(-9)+-開方(81-4*3*4)/2*3
x=9+-開方(33)/6

7,(x-3)(x+4)=2
x^2+4x-3x-12=2
x^2+x-14=0
x=-1+-開方(1^2-4*1*-14)/2
x=-1+-開方(57)/2

8,2x^2-4x-1=0
x=-(-4)+-開方(16-4*2*-1)/2*2
x=4+-開方(24)/4
x=2+-開方(6)/2

1.(2p+7)(p-3)=2p
2p2-6p+7p-2p-21=0
2p2-p-21=0
(2p-7)(p+3)=0
2p-7=0 or p+3=0
p=7/2 or p=-3

2.(a+1)(4a-5)=3a-2
4a2-5a+4a-5-3a+2=0
4a2-4a-3=0
(2a-3)(2a+1)=0
2a-3=0 or 2a+1=0
a=3/2 or a=-1/2

3.(x-2)2=36
x2-4x+4-36=0
x2-4x-32=0
(x-8)(x+4)=0
x-8=0 or x+4=0
x=8 or x=-4

4.(a+2/5)2=64
a2+4a/5+4/25-64=0
a2+4a/5-1596/25=0
(5a-38)(5a+42)=0
5a-38=0 or 5a+42=0
a=38/5 or a=-45/5

5.(x+2)2=5
x2+4x+4-5=0
x2+4x-1=0
x=(-(4)±√(( 4)2-4*1*-1))/(2*1)
x=(-4±√(20))/(2)
x=(-4±2√(5))/(2)
x=-2±√(5)

6.3x2-9x+4=0
x=(-(-9)±√((-9)2-4*3*4))/(2*3)
x=(9±√(33))/(6)

7.(x-3)(x+4)=2
x2+4x-3x-12-2=0
x2+x-14=0
x=(-(1)±√((1)2-4*1*-14))/(2*1)
x=(-1±√(57))/(2)

8.2x2-4x-1=0
x=(-(-4)±√((-4)2-4*2*-1))/(2*2)
x=(4±√(24))/(4)
x=(4±2√(6))/(4)
x=(2±√(6))/2