Question

if a square +b square+c square-ab-bc-ca=0,prove that a=b=c

Answer 1

${a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca = 0 \\ or \: \: 2( {a}^{2} + {b}^{2} + {c}^{2} ) - 2( ab+bc + ca) = 0 \\ or \: \: {(a - b)}^{2} + {(b - c)}^{2} + {(c - a)}^{2} = 0 \\ so \: we \: have \\ a = b \\ b = c \\ c = a$
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