Tính giá trị của biểu thức???

V

vipboycodon

A = $\dfrac{x^2}{x^2-y^2-z^2}+\dfrac{y^2}{y^2-z^2-x^2}+\dfrac{z^2}{z^2-x^2-y^2}$
= $\dfrac{x^2}{[ - (y+z) ]^2-y^2-z^2}+\dfrac{y^2}{[ - (x+z) ]^2-z^2-x^2}+ \dfrac{z^2}{[ - (x+y) ]^2-x^2-y^2}$
= $\dfrac{x^2}{2yz}+\dfrac{y^2}{2xz}+\dfrac{z^2}{2xy}$
= $\dfrac{x^3+y^3+z^3}{2xyz}$
= $\dfrac{3xyz}{2xyz} = \dfrac{3}{2}$
 
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