中二數學問題四條【求完整解答及說明】

1.
(a)
2500 m³
= 2500 × (100 cm)³
= 2.5 × 10⁹ cm³

(b)
1 cm³ = 1 mL

需時
= (2.5 × 10⁹) / (6.25 × 10⁸) 小時
= 4 小時


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2.
(a)
(5x² + ax - 6)(4x + 1)
= (5x² + ax - 6)4x + (5x² +ax - 6)
= 20x³ + 4ax² -24x + 5x² + ax - 6
= 20x³ + (4a + 5)x² +(a - 24)x - 6

(b)
4a + 5 = -23
4a = -28
a = -7


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3.
(a)
3x² - 8x - 16
= 3x² - 12x + 4x - 16
= (3x² - 12x) + (4x - 16)
= 3x(x - 4) + 4(x - 4)
= (3x + 4)(x - 4)

(b)
設 x = m + 1

3(m + 1)² - 8m - 24
= 3(m + 1)² - 8m - 8 - 16
= 3(m + 1)² - (8m + 8) - 16
= 3(m + 1)² - 8(m + 1) - 16
= 3x² - 8x - 16
= [3x + 4] [x - 4]
= [3(m + 1) + 4] [(m + 1) - 4]
= (3m + 3 + 4)(m + 1 - 4)
= (3m + 7)(m - 3)


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4.
太陽和地球的大約距離
= (3 × 10⁸) × (8 × 60) m
= 144 × 10⁹ m
= 1.44 × 10¹¹ m
= 1.44 × 10⁸ km

1a
2500 m^3
=2500*(100)^3 cm^3
=2.5*10^8 cm^3

1b
注滿泳池需要
=(2.5*10^8)/(6.25*10^8)
=0.4小時

2a
(5x^2 +ax-6)(4x+1)
=20x^3 +4ax^2 -24x +5x^2 +ax -6
=20x^3 +(4a+5)x^2 +(a-24)x -6

2b
x^2 的係數=-23
4x+5=-23
x=4.5

3a
3x^2 -8x -16
=(x-4)(3x+4)

3b
3(m+1)^2 -8m -24
=3(m+1)^2 -8m -16 -8
=3(m+1)^2 -8(m+1) -16
=[(m+1)-4][3(m+1)+4]
=(m-3)(3m+7)

4
太陽與地球的太約距離
=(3*10*8)(8*60)
=1.44*10^11