tìm x,y biết |x-y|+|y+9/25|=0

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1. Vì : $|x-y|$ $≥$ $0$ $∀$ $x;y$

         $|y+\dfrac{9}{25}|$ $≥$ $0$ $∀$ $y$

   Mà $|x-y| + |y + \dfrac{9}{25}| = 0$

   $⇒$ $\left \{ {{x-y=0} \atop {y+\dfrac{9}{25}=0}} \right.$

   $⇔$ $\left \{ {{x-y=0} \atop {y=-\dfrac{9}{25}}} \right.$

   $⇔$ $\left \{ {{x-(-\dfrac{9}{25})=0} \atop {y=-\dfrac{9}{25}}} \right.$

   $⇔$ $\left \{ {{x+\dfrac{9}{25}=0} \atop {y=-\dfrac{9}{25}}} \right.$

   $⇔$ $\left \{ {{x=-\dfrac{9}{25}} \atop {y=-\dfrac{9}{25}}} \right.$

       Vậy $x=y=\dfrac{-9}{25}$.

    

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2. Do  $\left \{ {{|x – y| ≥ 0 } \atop {|y + \frac{9}{25} | ≥ 0}} \right.$

   Mà: |x – y| + |y + $\frac{9}{25}$| = 0

   ⇒  $\left \{ {{|x – y| = 0 } \atop {|y + \frac{9}{25} | = 0}} \right.$

   ⇒  $\left \{ {{x – y = 0 } \atop {y + \frac{9}{25}  = 0}} \right.$

   ⇒  $\left \{ {{x – \frac{-9}{25} = 0 } \atop {y = \frac{-9}{25} }} \right.$

   ⇒  $\left \{ {{x + \frac{9}{25} = 0 } \atop {y = \frac{-9}{25} }} \right.$

   ⇒  $\left \{ {{x = \frac{-9}{25}  } \atop {y = \frac{-9}{25} }} \right.$

   Vậy x = y = $\frac{-9}{25}$

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