幫幫手﹏plz!!

(a) x^4 - 3x^2 - 4 =0
(x^2 - 4)(x^2 + 1) = 0
x^2 = 4 or x^2 = -1 (rejected)
x = 2 or x = -2

(b) x-4/x=2
x-4 = 2x
x = -4

(c) sqrt(x-1) =x-3
x-1 = (x-3)^2
x-1 = x^2 - 6x + 9
x^2 - 7x + 10 = 0
(x - 2)(x - 5) = 0
x = 2 or x = 5
當 x = 2,
L.H.S = sqrt(1) = 1
R.H.S. = 2-3 = -1
rejected
當 x = 5,
L.H.S = sqrt(4) = 2
R.H.S. = 5-3 = 2
所以 x = 5

(d) (x+1)^2 - 4(x+1) - 5=0
[ (x+1) - 5 ] [ (x+1) + 1 ] = 0
(x - 4)(x + 2) = 0
x = 4 or x = -2

(e)
y=x^2-2x-3
x+y-3=0
y = -x + 3
-x + 3 = x^2-2x-3
x^2-x-6 = 0
(x - 3)(x + 2) = 0
x = 3 or x = -2
x = 3 , y = 0
x = -2, y = 5
(3, 0), (-2, 5)


(f)
3x^2+2y+1=0
3y-4x=41
y = (4x + 41) / 3
3x^2+2(4x + 41) / 3+1=0
9x^2 + 2(4x + 41) +3=0
9x^2 + 8x + 85=0
無根,
係咪打錯野,計唔到


(g) 3/(x-1) + (x+1)/(x+3) = 8/(x^2+2x-3)
3/(x-1) + (x+1)/(x+3) = 8/[ (x-1) (x+3) ]
[ 3(x+3) + (x+1)(x-1) ] / [ (x-1) (x+3) ] = 8/[ (x-1) (x+3) ]
3(x+3) + (x+1)(x-1) = 8
x^2 + 3x + 8 = 8
x^2 + 3x = 0
x(x + 3) = 0
x = 0 or x = -3 (rejected, 因為令分母變零)

(h) x+2x/(x-3) = 6/(x-3)
x(x-3) + 2x = 6
x^2 -x - 6 = 0
(x - 3)(x + 2) = 0
x = 3 (rejected, 令分母變零) or x = -2
2)
每個橙原本的售價 = 96/k
調低＄２,即新價 (96/k - 2), 可買 (k+4) 個橙,所以
(96/k - 2)(k+4) = 96
(96 - 2k)(k+4) = 96k (全式乘 k)
-2k^2 + 88k + 384 = 96k
2k^2 - 8k - 384 = 0
k^2 - 4k - 192 = 0
(k - 16)(k + 12) = 0
k = 16 or k = -12 (rejected)

好多, 做死人

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