二次方程..明天考試,感謝!幫幫忙!

2009-01-19 11:04 pm
下面有d數,我知簡單果d點計,但係呢種類型唔識..解釋長盡d.steps

1. 如果8(x-3)=3x-x^2, 求x-1的值

2. 如果(x-2)(x-3)=0, (x+1)(x+2)=?

3. 3^x=36-3^x-1 x=?

上述幾種題型唔係好清楚,希望大家解答同解釋一下!!!

回答 (3)

2009-01-19 11:21 pm
✔ 最佳答案
1) 8(x-3)=3x-x^2
8x-24=3x-x^2
x^2+8x-3x-24
x^2+5x-24=0
(x-3)(x+8)=0

so x-3=0 or x+8=0
x=3 or x=-8

if x=3
then x-1=3-1=2

if x=-8
then x-1=-8-1=-9

2)(x-2)(x-3)=0
so x-2=0 or x-3=0
x=2 or x=3

if x=2
then (x+1)(x+2)=(2+1)(2+2)=3*4=12

if x=3
then (x+1)(x+2)=(3+1)(3+2)=4*5=20

3) 3^x=36-3^x-1
3^x+3^x-1=36
3^x(1+1/3)=36
3^x(4/3)=36
3^x=36(3/4)
3^x=27
3^x=3^4<-----27=3的4次方
x=4

2009-01-19 18:50:30 補充:
sorry
第三題的答案係3
因為3^3=27
2009-01-19 11:47 pm
1) 8(x-3)=3x-x^2
8x-24=3x-x^2
x^2+8x-3x-24
x^2+5x-24=0
(x-3)(x+8)=0

so x-3=0 or x+8=0
x=3 or x=-8

if x=3
then x-1=3-1=2

if x=-8
then x-1=-8-1=-9

2)(x-2)(x-3)=0
so x-2=0 or x-3=0
x=2 or x=3

if x=2
then (x+1)(x+2)=(2+1)(2+2)=3*4=12

if x=3
then (x+1)(x+2)=(3+1)(3+2)=4*5=20

3) 3^x=36-3^x-1
3^x+3^x-1=36
3^x(1+1/3)=36
3^x(4/3)=36
3^x=36(3/4)
3^x=27
3^x=3^4<-----27=3的4次方
x=4
參考: ^&^ me~~~~~~~~~~~~^&^0.0~~~~~~030
2009-01-19 11:12 pm
1
8(x-3)=3x-x^2
x^2-3x+8x-24=0
x^2+5x-24=0
(x+8)(x-3)=0
x=3 or -8
2
(x-2)(x-3)=0
x=2 or 3
when x=2
(x+1)(x+2)=12
when x=3
(x+1)(x+2)=20
3^x=36-3^(x-1)
3^(x-1)+3^x=36
3^(x-1)(1+3)=36
3^(x-1)=9
x=3


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