if (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0
3x2-2x(a+b+c)+(ab+bc+ca)=0
this is quardadic equation so we will find D
4(a+b+c)2-12(ab+bc+ca)=4[(a+b+c)2-3(ab+bc+ca)]=4{a2+b2+c2-ab+bc+ca}
which is equal to
4/2{ (a-b)2+(b-c)2+(c-a)2} which is greater than 0
so the roots of this equation are real.
Moderation Team
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