\(\dfrac{x+1}{65}+1+\dfrac{x+3}{63}+1=\dfrac{x+5}{61}+1+\dfrac{x+7}{59}+1\)

\(\Leftrightarrow\dfrac{x+66}{65}+\dfrac{x+66}{63}-\dfrac{x+66}{61}-\dfrac{x+66}{59}=0\)

\(\Leftrightarrow\left(x+66\right)\left(\dfrac{1}{65}+\dfrac{1}{63}-\dfrac{1}{61}-\dfrac{1}{59}\ne0\right)=0\Leftrightarrow x=-66\)

\(\left(x^2+y^2-5\right)-\left(2xy-4\right)^2=\left(x^2+y^2-1-2xy\right)^2=\left[\left(x-y\right)^2-1\right]^2=\left(x-y-1\right)^2\left(x-y+1\right)^2\)

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Với x > = 0 ; x khác 4 

\(A=\dfrac{9+2x+\sqrt{x}-10-x+1}{x-\sqrt{x}-2}=\dfrac{x+\sqrt{x}}{x-\sqrt{x}-2}=\dfrac{\sqrt{x}}{\sqrt{x}-2}\)

\(=\dfrac{\sqrt{x}-2+2}{\sqrt{x}-2}=1+\dfrac{2}{\sqrt{x}-2}\Rightarrow\sqrt{x}-2\inƯ\left(2\right)=\left\{\pm1;\pm2\right\}\)

\(=\dfrac{\sqrt{3}\left(\sqrt{3}+2\right)}{\sqrt{3}}+\dfrac{\sqrt{2}\left(\sqrt{2}+1\right)}{\sqrt{2}+1}-\sqrt{3}+2\)

\(=\sqrt{3}+2+\sqrt{2}-\sqrt{3}+2=4+\sqrt{2}\)