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簡單的數學，不等式+絕對值的計算

Sep 8th 2013, 09:03

好吧，那我算頭三題。

1.解不等式
(2x-1)<x+4
2x-x<4+1
x<5
你說答案有 x > -1，那相信是因為有其他條件限制，你可以看漏了。

2.解不等式
（1-x)≧1 變成 -x≧0 變成 x ≤ 0
（x+2)<5 變成 x < 3
如果兩條件均要成立，則要 x ≤ 0

3.設x.y滿足-2≦x≦5 1≦y≦3
求下列各數的範圍
(1)2x+3y
-4≦2x≦10　和 3≦3y≦9
-1 ≦ 2x+3y ≦ 19

(2)2x-3y
-4≦2x≦10　和 3≦3y≦9 即 -9≦-3y≦-3
2x-3y即2x+(-3y)
-13 ≦ 2x-3y ≦ 7

(3)xy
-2≦x≦5 1≦y≦3
最小會是負數 x 取 -2, y取最大的正數3。
最大會是正數，今次不能負負得正，只能兩者取最大。
-6 ≦ xy ≦ 15

(4)x²+y²
-2≦x≦5 即 0 ≦ x² ≦ 25　前者經過０，所以最小值是０。
1≦y≦3 即 1 ≦ y² ≦ 9
1 ≦ x²+y² ≦ 34

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