Question

cho a + b + c = 0

Tính : \(A=\frac{a^2}{bc}+\frac{b^2}{ac}+\frac{c^2}{ab}\)

 

Answer 1

\(A=\frac{a^3+b^3+c^3}{abc}\)

\(a+b+c=0\Rightarrow c=-\left(a+b\right)\)

\(\Rightarrow a^3+b^3+c^3=a^3+b^3-\left(a+b\right)^3=-3ab\left(a+b\right)=3abc\)

\(\Rightarrow A=\frac{3abc}{abc}=3\)

Answer 2

\(A=\frac{a^3+b^3+c^3}{abc}=\frac{\left(a+b+c\right)\left(a^2+b^2+c^2-ab-bc-ca\right)+3abc}{abc}=\frac{3abc}{abc}=3\)