Question

1. Giải phương trình ẩn x sau: \(x^3\)- ( a+b+c ) \(x^2\) = -( ab+ac+bc) x + abc

Answer 1

\(x^3-\left(a+b+c\right)x^2+\left(ab+bc+ca\right)x-abc=0\)

\(\Leftrightarrow\left(x^3-ax^2\right)-\left(bx^2-abx\right)-\left(cx^2-cax\right)+\left(bcx-abc\right)=0\)\(\Leftrightarrow x^2\left(x-a\right)-bx\left(x-a\right)-cx\left(x-a\right)+bc\left(x-a\right)=0\)

\(\Leftrightarrow\left(x-a\right)[\left(x^2-bx\right)-\left(cx-bc\right)]=0\)

\(\Leftrightarrow\left(x-a\right)\left(x-b\right)\left(x-c\right)=0\)

Từ đó: \(S=\left\{a;b;c\right\}\)