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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 9: rút gọn A= x √x + y √y / √x + √y – ( √x – √y) ² (x ≥0; y ≥0 ; x khác y

Toán Lớp 9: rút gọn A= x √x + y √y / √x + √y – ( √x – √y) ² (x ≥0; y ≥0 ; x khác y

Comments ( 2 )

  1. (x\sqrt{x}+y\sqrt{y})/(\sqrt{x}+\sqrt{y})-(\sqrt{x}-\sqrt{y})^2
    =((\sqrt{x}+\sqrt{y})(x-\sqrt{xy}+y))/(\sqrt{x}+\sqrt{y})-(x-2\sqrt{xy}+y)
    =x-\sqrt{xy}+y-x+2\sqrt{xy}-y
    =(x-x)+(y-y)-(\sqrt{xy}-2\sqrt{xy})
    =\sqrt{xy}
     

  2. $A=\dfrac{x\sqrt{x}+y\sqrt{y}}{\sqrt{x}+\sqrt{y}}-(\sqrt{x}-\sqrt{y})^2$
    $=\dfrac{\sqrt{x}^3+\sqrt{y}^3}{\sqrt{x}+\sqrt{y}}-(x-2\sqrt{xy}+y)$
    $=\dfrac{(\sqrt{x}+\sqrt{y})(x-\sqrt{xy}+y)}{\sqrt{x}+\sqrt{y}}-x+2\sqrt{xy}-y$
    $=x-\sqrt{xy}+y-x+2\sqrt{xy}-y$
    $=\sqrt{xy}$

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222-9+11+12:2*14+14 = ? ( )