Mathematics Questions

1.
(a)
L1 : 3x + 7y - 11 = 0 ...... [1]
L2 : 4x + 3y - 2 = 0 ...... [2]

[1]*4 - [2]*3 :
19y - 38 = 0
y = 2

Put y = 2 into [2] :
4x + 3(2) - 2 = 0
x = -1

Hence, the coordinates of A = (-1, 2)

(b)
L3 passes through (-1, 2) and (0, -3).

The equation of L3 :
(y + 3)/(x - 0) = (2 + 3)/(-1 - 0)
(y + 3)/x = -5
y + 3 = -5x
5x + y + 3 = 0


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2.
√3(2√3 - √6)
= 2√9 - √18
= 2√3² - √(3²x2)
= 6 - 3√2


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3.
(5 + √7)² = a + b√7
5² + 2x5x√7 + (√7)² = a + b√7
32 + 10√7 = a + b√7

Hence, a = 32 and b = 10

1. (a)用聯立二元一次solveL1同L2, x = -1, y = 2, A(-1, 2).
(b)用2-points form,
(y - 2)/[x - (-1)] = [2 - (-3)]/[(-1) - 0]
5x + y + 3 = 0
2. 睇唔明
3. 唔識

2012-08-13 17:30:18 補充：
3. (5 + √7)² ≡ a + b√7
L.H.S.
= (5 + √7)²
= 5² + (2)(5)(√7) + (√7)²
= 32 + 10√7
∴ a = 32, b = 10.