Question

[Tuấn Huy Trương]

Tính:   A = x².y².z²     

Biết x,y,z là các số thực thỏa mãn:

\(\dfrac{1}{x^2\left(y-z\right)}\)=\(\dfrac{-3}{5}\)

\(\dfrac{1}{y^2\left(z-x\right)}\)=\(\dfrac{1}{3}\)

\(\dfrac{1}{z^2\left(x-y\right)}\)= 3

Answer 1

[Nguyễn Ngọc Anh Minh]

\(\dfrac{1}{x^2\left(y-z\right)}=-\dfrac{3}{5}\Rightarrow x^2=-\dfrac{5}{3\left(y-z\right)}\)

\(\dfrac{1}{y^2\left(z-x\right)}=\dfrac{1}{3}\Rightarrow y^2=\dfrac{3}{\left(z-x\right)}\)

\(\dfrac{1}{z^2\left(x-y\right)}=3\Rightarrow z^2=\dfrac{1}{3\left(x-y\right)}\)

\(A=x^2.y^2.z^2=-\dfrac{5}{3\left(y-z\right)}.\dfrac{3}{z-x}.\dfrac{1}{3\left(x-y\right)}=\)

\(=-\dfrac{5}{3}.\dfrac{1}{\left(y-z\right)\left(z-x\right)\left(x-y\right)}=\)