章不等式解答chapter 13 inequalities solutions13.pdfVIP

SolutionsforChapter13:Inequalities

1.[MJC/Prelim2010/P2/1]

x+7

≤1

4+3x−x2

x+7

−1≤0

4+3x−x2

2

x+7−(4+3x−x)

≤0

2

4+3x−x

x+7−4−3x+x2

≤0

−(x2−3x−4)

2

x−2x+3

≥0

2

x−3x−4

Sincex2−2x+3=(x−1)2+20forx∈,

x2−3x−40

(x−4)(x+1)0

x−1orx4

2.[SRJC/Prelim2010/P1/1]

2x2+x3

−32x2+x3

−32x2+xand2x2+x3

2x2+x+30and2x2+x−30

2

123

x++0and(2x+3)(x−1)0

416

3

x∈and−x1

2

3

x∈:−x1

Takingtheintersection,thesolutionsetis2

2

111



xxx

2ex+e232e2+e23







1

x

2

∴replacexwithe

11

3xx

−e2e2(sinceexisalwayspositive)

101

2