Question

a,C/M:\(\dfrac{2-\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}{2-\sqrt{2+\sqrt{2+\sqrt{2}}}}< \dfrac{1}{3}\)

b,tìm các số nguyên x,y thoa mãn \(x^2+x+2y^2+y=2xy^2xy+3\)

Answer 1

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

\(\Leftrightarrow\dfrac{4-2-\sqrt{2+\sqrt{2+\sqrt{2}}}}{(2-\sqrt{2+\sqrt{2+\sqrt{2}}})\left(2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}\right)}< \dfrac{1}{3}\)

\(\Leftrightarrow\dfrac{1}{\left(2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}\right)}< \dfrac{1}{3}\)

\(\Leftrightarrow2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}>3\)

\(\Leftrightarrow\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}>-1\left(đúng\right)\)

\(\Rightarrowđpcm\)

Answer 2

sao lại 2xy^2xy