✔ 最佳答案
1. 1/x : 1/y = 4 : 5, that is (1/x)/(1/y) = 4/5, y/x = 4/5, that is y : x = 4 : 5.....(1).
Similarly, 1/x : 1/z = 4 : 2, that is (1/x)/(1/z) = 4/2 , z/x = 4/2, that is z : x = 4 : 2 ....(2).
From (1), y : x = 4 : 5 = 8 : 10
From (2), z : x = 4 : 2 = 20 : 10.
So x : y : z = 10 : 8 : 20 = 5 : 4 : 10.
2.
3/x : 9/(x + 1) = 2 : 3. That is [3/x]/[9/(x + 1)] = 2/3
(x + 1)/3x = 2/3
3(x + 1) = 6x
3x + 3 = 6x, so x = 1.
3.
a : b = 1 : 5, so a/b = 1/5, that is b = 5a ..........(1)
a : c = 3 : 1, so a/c = 3/1, that is c = a/3..........(2)
Therefore, 2a + 5a - a/3 = 60
6a + 15a - a = 180
20a = 180, a = 9, b = 5a = 45, c = a/3 = 3.
Factorize :
(a) 12 - 3(e + 2f)^2 = 3[4 - (e + f)^2] = 3(2 + e + f)(2 - e -f).
(b) 98(g - h)^2 - 50g^2 = 2[49(g - h)^2 - 25g^2] = 2[7(g - h) + 5g][7(g - h) - 5g] = 2(12g - 7h)(2g - 7h).
(c) x^4 - 1 = [x^2]^2 - 1^2 = (x^2 - 1)(x^2 + 1) = (x + 1)(x - 1)(x^2 + 1).
(d) 1 - 4c^2 - 9d^2 + 36c^2d^2 = (1 - 4c^2) - 9d^2(1 - 4c^2)
= (1 - 4c^2)(1 - 9d^2) = (1 - 2c)(1 + 2c)(1 - 3d)(1 + 3d).
