Đặt \(\sqrt[3]{1-x}=a;\text{ }\sqrt[3]{1+x}=b\Rightarrow a^3+b^3=2\)
Pt đã cho trở thành \(a+b=1\Leftrightarrow b=1-a\)
Suy ra: \(a^3+\left(1-a\right)^3=2\Leftrightarrow3a^2-3a-1=0\Leftrightarrow a=\frac{3\pm\sqrt{21}}{6}\)
\(\Leftrightarrow\sqrt[3]{1-x}=\frac{3\pm\sqrt{21}}{6}\Leftrightarrow x=1-\left(\frac{3\pm\sqrt{21}}{6}\right)^3\)
giai p.t :\(\sqrt{\frac{x^3+1}{x+3}}+\sqrt{x+1}=\sqrt{x^2-x+1}+\sqrt{x+3}\)
giai p.t : \(x\sqrt{x^2-x+1}+4\sqrt{3x+1}=x^2+x+3\)
giai p.t : \(\sqrt{x+1}-\sqrt{x-7}=\sqrt{12-x}\)
giai p.t \(\frac{36}{\sqrt{x-2}}+\frac{4}{\sqrt{y-1}}=28-4\sqrt{x-2}-\sqrt{y-1}\)
giai p.t :\(\sqrt{x}+2\sqrt{x+3}=x+4\)
giai p.t : \(\frac{1}{x}+\frac{1}{\sqrt{2-x^2}}=2\)
giai p.t :\(\sqrt{2x^2+x+6}+\sqrt{x^2+x+2}=x+\frac{4}{x}\)
giai phuong trinh
\(\frac{1}{\sqrt{x}+\sqrt{x+1}}+\frac{1}{\sqrt{x+1}+\sqrt{x+2}}+\frac{1}{\sqrt{x+2}+\sqrt{x+3}}=1\)
giai phương trình
(x+1)(x+2) = 3 \(\sqrt{x\left(x+3\right)}\)
(\(\sqrt{x+4}\)-2)(\(\sqrt{4-x}\) +2) = 2x
