Question

Tìm m,n thuộc Z sao cho : n^2=(m+1)^3-m^3

Answer 1

\(n^2=(a+1)^3-a^3\)

\(n^2+3(a+1)a=(a+1)^3-a^3+3(a+1)a\)

\(n^2+3(a+1)a=(a+1-a)^3\)

\(n^2+3(a+1)a=1^3=1\)

\(n^2\ge0(\forall n);a\inℤ;n\inℤ\)

\(\Rightarrow a+1=0;a=0;n^2=1\)

\(\Rightarrow a=-1;a=0;n=1;n=-1\)

Answer 2

m = -1;m = 0
n = -1;n = 0
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