Question

cho a²+b²+c²=00. CMR A=B=C với A= a².(a²+b²).(a²+c²); B=b².(b²+c²).(b²+a²);C=c².(c²+a²).(c²+b²)

Answer 1

Ta có: \(a^2+b^2+c^2=0\)

=>\(b^2+c^2=-a^2;a^2+b^2=-c^2;a^2+c^2=-b^2\)

Ta có: \(A=a^2\left(a^2+b^2\right)\left(a^2+c^2\right)\)

\(=a^2\cdot\left(-c^2\right)\cdot\left(-b^2\right)=a^2b^2c^2\left(1\right)\)

Ta có: \(B=b^2\left(b^2+c^2\right)\left(b^2+a^2\right)\)

\(=b^2\cdot\left(-a^2\right)\cdot\left(-c^2\right)=b^2a^2c^2\) (2)

Ta có: \(C=c^2\left(c^2+a^2\right)\left(c^2+b^2\right)\)

\(=c^2\left(-b^2\right)\cdot\left(-a^2\right)=a^2b^2c^2\) (3)

Từ (1),(2),(3) suy ra A=B=C