Đặt a=\(\sqrt[3]{\sqrt{2}-1}\Rightarrow x^3=\sqrt{2}-1\)
b=\(\sqrt[3]{\sqrt{2}+1}\Rightarrow b^3=\sqrt{2}+1\)
\(\Rightarrow x=a-b\)
\(\Rightarrow x^3=\left(a-b\right)^3\)
\(\Leftrightarrow x^3=a^3-3a^2b+3ab^3-b^3\)
\(\Leftrightarrow x^3=a^3+b^3-3ab\left(a-b\right)\)
\(\Leftrightarrow x^3=\sqrt{2}-1-\sqrt{2}-1-3\sqrt[3]{\sqrt{2}-1}\cdot\sqrt[3]{\sqrt{2}+1}x\)
\(\Leftrightarrow x^3=-2-3\sqrt[3]{2-1}x\)
\(\Leftrightarrow x^3=-2-3x\)
\(\Leftrightarrow x^3+3x=-2\)
\(\Leftrightarrow x^3+3x+5=3\)
Hay A=3
\(x^3=\sqrt{2}-1-\sqrt{2}-1-3x\sqrt[3]{2-1} \)
<=>\(x^3+3x+2=0\)
<=>\(x^3+3x+5=3\)
<=>A=3
