Question 153004
{{{(x-a)(x-b)+(x-b)(x-c)+(x-a)(x-c)=0}}} Start with the given equation.



{{{(x-a)(x-a)+(x-a)(x-a)+(x-a)(x-a)=0}}} Plug in {{{b=a}}} and {{{c=a}}}



{{{x^2-2ax+a^2+x^2-2ax+a^2+x^2-2ax+a^2=0}}} FOIL



{{{3x^2-6ax+3a^2=0}}} Combine like terms.



{{{3(x-a)^2=0}}} Factor the left side



{{{(x-a)^2=0}}} Divide both sides by 3.



{{{x-a=0}}} Take the square root of both sides.



{{{x=a}}} Add "a" to both sides.



So the expression {{{(x-a)(x-b)+(x-b)(x-c)+(x-a)(x-c)}}} has a root of {{{x=a}}} (with a multiplicity of 2) if {{{a=b=c}}}