急 F5 Inequalities Unknown2C03

2012-08-21 3:51 am

請詳細講解以下兩條問題 :(不要網址回答) Solve each of the following quadratic inequalities graphically and represent the solutions on the number line : 1. 2x(s+6)>=(3x+2)(x+2)我計法 : 0>= x^2+4x4 0>=(x-2)(x-2) x<=2 正確答案 : x=2 [甚麼情況用這個做答案,點解 ?] 2. a) -4x^2<=49-28x我計法 : 0<=4x^2-28x+49 (2x-7)(2x-7)>=0 x>=7/2正確答案 : any real number [同上一題相似有兩個相同答案,點解咁答 ?] b) Hence, solve -4x^2<=49-28x正確答案 :no solutions [點解 ? ]

回答 (1)

kimkay

2012-08-21 7:31 am

✔ 最佳答案

當a>0且α>β時,
a(x-α)(x-β)>0,解為x<β or x>α
a(x-α)(x-β)≧0,解為x≦β or x≧α
a(x-α)(x-β)<0,解為β<x<α
a(x-α)(x-β)≦0,解為β≦x≦α

1.
2x(x+6)≧(3x+2)(x+2)
2x^2+12x≧3x^2+6x+2x+4
0≧3x^2+6x+2x+4-(2x^2+12x)
0≧3x^2+8x+4-2x^2-12x
0≧x^2-4x+4
0≧(x-2)(x-2)
(x-2)(x-2)≦0
2≦x≦2 x大於或等於2和x小於或等於2,因此x=2.
2.
-4x^2≦49-28x
0≦4x^2-28x+49
0≦(2x-7)^2
(2x-7)^2≧0 當x=7/2時=0,x<7/2時和x>7/2時這不等式都成立
3.
-4x^2≦49-28x
0≦4x^2-28x+49
△=b^2-4ac (-28)^2-4×4×49=0

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