Question

Answer 1

\(A=\frac{a^2}{bc}+\frac{b^2}{ac}+\frac{c^2}{ab}\)
\(=\frac{a^3}{abc}+\frac{b^3}{abc}+\frac{c^3}{abc}=\frac{a^3+b^3+c^3}{abc}\)
Ta có:
\(a^3+b^3+c^3\)
\(=a^3+b^3+\left\lbrack-\left(a+b\right)\right\rbrack^3\) \(\)
\(=a^3+b^3-\left\lbrack a^3+b^3+3ab\left(a+b\right)\right\rbrack\)
\(=a^3+b^3-\left(a^3+b^3\right)-3ab\left(a+b\right)\)
\(=-3ab\left(a+b\right)\)
\(=-3ab\left(-c\right)\)
\(=3abc\)
Thay \(a^3+b^3+c^3\) vào A, ta có:
\(A=\frac{3abc}{abc}=3\)