F.2 數學題 (((((((20點)))))))

1a)ab + bc + 2a + 2c = a(b+2)+c(b+2) = (b+2)(a+c)
1b)3-12s^2 = 3(1-4s^2) = 2(1-2s)(1+2s)
1c) x^2 - 18 + 81 = (x)^2 -2(x)(9) +(9)^2 =(x-9)^2
1d) 9x^2 + 24x + 16 = (3x)^2 +2(3x)(4) +(4)^2 =(3x+4)^2

2a) a^2-ab/ab-b^2 = a(a-b)/b(a-b) = a/b
2b) 1/4a + 3/2a = 1/4a +6/4a = 7/4a
2c) 2x/3x+y - x+y/-y-3x = 2x/3x+y + x+y/3x+y = 3x+y/3x+y =1

3a) y - 1/3x + 1/4x = 2y [x]
-4/12x+3/12x = y
-1/12x = y
x = -12y
3b) 1/2a + 1/4b - 1/3a = b [a]
3/6a - 2/6 a = 3/4b
1/6a = 3/4b
a = 9/2b
4a) 開方根15 / 開方根2 = 開方根15 / 開方根2 * 開方根2 / 開方根2
=開方根30 / 2
5a) 3開方根12 + 2開方根27 = 3開方根12 + 2開方根27
=3(2開方根3)+2(3開方根3)
=6開方根3+6開方根3
=12開方根3
6a){ 2x - 3y = 7 ------(1)
{ 3x - 7y = 23-----(2)
(1)*3 , 6x -9y = 21-----(3)
(2)*2 , 6x -14y = 46------(4)
(4)-(3) , -5y = 25
y = -5
put y=-5 into (1) , 2x-3(-5) = 7
2x+15 = 7
2x = -4
x = -2
therefore x = -2 , y = -5

7{ 3x - 4y = 20 --------(1)
{ 4y - x = -4 --------(2)
(2)*3 , 12y-3x = -12
(1)+(2) , 8y = 8
y = 1
put y = 1 into (2), 4-x = -4
x = 8
therefore x = 8 , y = 1

8 let grades B tea in the mixture be x g
grades A tea in the mixture be (1800 - x)g 因為1.8kg=1800g
84x + 120(1800 -x) = 1800(100)
84x + 216000 -120x = 180000
36x = 36000
x = 1000
grades B tea in the mixture =1000g
gradesA tea in the mixture = 800g
Therefore,grade B tea heavier than the grade A tea in the mixture = 1000g-800g
=200g

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a) ab + bc + 2a + 2c
=a(b+2)+c(b+2)
=(a+c)(b+2)
b) 3-12s^2
=3(1-4s^2)
=3{(1^2-(2s)^2}
=3(1+2s)(1-2s)
c) x^2 - 18 + 81
=x^2+2(x)(9)+9^2
=(x+9)^2
d) 9x^2 + 24x + 16
3x 4
3x 4
上為十字相乘

a) a^2-ab/ab-b^2
=a^2-b^2-1
=(a+b)(a-b)-1
b) 1/4a + 3/2a
=7/4a