(a+b+c)²=a²+b²+c²+2(ab+ac+bc)⇒2(ab+ac+bc)=(a+b+c)²-(a²+b²+c²)⇒
2(ab+ac+bc)=12²-50=144-50=[tex](-a+b+c)^2 =\mathbf{a^{2} - 2 \; a \; b - 2 \; a \; c + b^{2} + 2 \; b \; c + c^{2}}\\
( a-b+c)^2=\mathbf{a^{2} - 2 \; a \; b + 2 \; a \; c + b^{2} - 2 \; b \; c + c^{2}}\\
(a+b-c)^2=\mathbf{a^{2} + 2 \; a \; b - 2 \; a \; c + b^{2} - 2 \; b \; c + c^{2}}\\
(-a+b+c)^2 + ( a-b+c)^2 + (a+b-c)^2=\\
=\mathbf{3 \; a^{2} - 2 \; a \; b - 2 \; a \; c + 3 \; b^{2} - 2 \; b \; c + 3 \; c^{2}}=\\
=3(a^2+b^2+c^2)-2(ab+ac+bc)=\\
=3\cdot 50-94=\\
=150-94=\\ =56\\
[/tex]
