配方法應用題 (8條)

1．9(y-1)^2-144=0
[3(y-1)]^2 - 12^2 = 0
(3y-3-12)(3y-3+12) = 0
(3y - 15)(3y + 9) = 0
(y - 5)(y + 3) = 0
y = 5 or -3
2．7(x+4)^2+28=0
(x+4)^2 + 2^2 = 0
(x+4+2)(x+4-2) = 0
(x+6)(x+2) = 0
x = -6 or -2
3．4(x+1)^2+25=0
[2(x+1)]^2 + 5^2 = 0
(2x+2+5)(2x+2-5) = 0
(2x + 7)(2x - 3) = 0
x = -7/2 or 3/2
4．4(x-5)^2-49=0
[2(x-5)]^2 - 7^2 = 0
(2x-10-7)(2x-10+7) = 0
(2x-17)(2x-3) = 0
x = 17/2 or 3/2
5．4y^2-15y+9=0
(y - 3)(4y - 3) = 0
y = 3 or 3/4
6．18y^2-25y-3=0
(2y-3)(9y+1) = 0
y = 3/2 or -1/9
7．56(5x+7)+48x^2=0
7(5x+7) + 6x^2 = 0
6x^2 + 35x + 49 = 0
(2x+7)(3x+7) = 0
x = -7/2 or -7/3
8．92x(x+3)=161
4x(x+3) = 7
4x^2 + 12x - 7 = 0
(2x-1)(2x+7) = 0
x = 1/2 or -7/2


2010-09-11 20:47:25 補充：
2．7(x+4)^2-28=0
(x+4)^2 + 2^2 = 0
(x+4+2)(x+4-2) = 0
(x+6)(x+2) = 0
x = -6 or -2
3．4(x+1)^2-25=0
[2(x+1)]^2 + 5^2 = 0
(2x+2+5)(2x+2-5) = 0
(2x + 7)(2x - 3) = 0
x = -7/2 or 3/2

2010-09-11 20:49:54 補充：
if it's not corrected,
For Q2.
7(x+4)^2+28=0
x^2 + 8x + 16 + 4 = 0
x^2 + 8x + 20 = 0
△ = 64 - 80 = -16 < 0
For Q3,
8(x+1)^2+25=0
8x^2 + 8x + 89 = 0
△ = 61 - 4(89) <0

2010-09-11 20:57:55 補充：
第2和第3題好像錯了呢
答案好像錯了<<< 黃色部分已改, 數式改動了才能得出x, 答案於第1次補充
否則, 請參照第2次補充, Q2 和 Q3 皆不可求出x的實根

2010-09-11 21:06:53 補充：
既然你學了虛數i,那x就可解了,只是不是實根罷了
For Q2.
7(x+4)^2+28=0
x^2 + 8x + 16 + 4 = 0
x^2 + 8x + 20 = 0
x = [-8+/-√(64-80)]/2
x = -4 +/- 2i

2010-09-11 21:09:54 補充：
For Q3,
8(x+1)^2+25=0
(x+1)^2 = -25/8
x+1 = +/-√(-25/8)
x = -1 +/- 5/2 √(i/2)

There should be no real solution in Q2, Q3