Question

Cho \(a,b,c\ne0\)và a - b + c = 0.

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

 

Answer 1

\(a-b+c=0\Rightarrow a=b-c;b=a+c;c=b-a\)

\(\Rightarrow a^2=b^2-2bc+c^2;b^2=a^2+2ac+c^2;c^2=b^2-2ab+a^2\)

\(\text{Suy ra: }\frac{ab}{a^2+b^2-c^2}+\frac{bc}{b^2+c^2-a^2}+\frac{ac}{a^2+c^2-b^2}\)

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

\(=\frac{a}{2.\left(b-c\right)}+\frac{b}{2.\left(a+c\right)}+\frac{c}{-2.\left(b-a\right)}\)

\(=\frac{a}{2a}+\frac{b}{2b}+\frac{c}{-2c}=\frac{1}{2}+\frac{1}{2}-\frac{1}{2}=\frac{1}{2}\)

Answer 2

2 

MINARIRO LAMARY

Answer 3

2 tích nhé