x2−22x3+x2−x−2
=x2−22x(x2−2)+(x2−2)+3x
=2x+1+x2−23x Given n∈Z+
n=1,2(1)+1+(1)2−23(1)=0,0∈Z
n≥2,x2−23x≥1
x2−2x2−3x−2≤0
x2−2x2−3x−2≤0
x2−3x−2=0
x1=23−17,x2=23+17
x∈(−2,23−17]∪(2,23+17] Since n is positive integer, we consider n=2,3.
n=2,n2−23n=(2)2−23(2)=3,integer
n=3,n2−23n=(3)2−23(3)=79,is not integer
n=1,n=3.
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