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#1 loga logb log(a+5) 是等差數列

logb-loga=log(a+5)-logb=(1/2)(log(a+5)-loga)
→2logb=loga(a+5)
→a^2+5a-b^2=0
→a=-5/2+√(25+4b^2) or -5/2-√(25+4b^2)
log裡面不能放負數，故僅考慮a=-5/2+[√(25+4b^2)]/2
則b是正整數且a是正整數
故b=6，a=4

#2 |x+2|-|x-4|>k有解

x>4
|x+2|-|x-4|>k
→x+2-x+4>k
→6>k

4≥x≥-2
|x+2|-|x-4|>k
→x+2+x-4>k
→2x-2>k
→x>k/2+1
注意：要使得 4≥x≥-2 和 x>k/2+1 不互相衝突
這表示 4>k/2+1→6>k

-2>x
|x+2|-|x-4|>k
→-x-2+x-4>k
→-6>k

綜合以上，要使得x有解的k可以是0, 2, 4
k不能是6因為嚴格大於並不包含等於

#3 用勘根定理
令f(x)=2x^3-5x-11
f 是連續的且 f(2)<0,f(3)>0
所以2x^3-5x-11=0其中的一根界於2和3之間
故該正根最接近的整數為2

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