Question

Cho a,b,c là 3 số chính phương.

Chứng minh ràng : P = (a-b)(b-c)(c-a) chia hết cho 12

Answer 1

\(a=x^2;b=y^2;c=z^2\)

\(P=\left(a-b\right)\left(b-c\right)\left(c-a\right)=\left(x^2-y^2\right)\left(y^2-z^2\right)\left(z^2-x^2\right)\)

\(=\left(x-y\right)\left(x+y\right)\left(y-z\right)\left(y-z\right)\left(z-x\right)\left(z+x\right)\)

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Answer 2

a=x2;b=y2;c=z2 P=(a−b)(b−c)(c−a)=(x2−y2)(y2−z2)(z2−x2) =(x−y)(x+y)(y−z)(y−z)(z−x)(z+x)