Đặt \(\hept{\begin{cases}\sqrt[3]{2-x}=b\\\sqrt{x-1}=a\end{cases}}\)
Ta có hệ \(\hept{\begin{cases}a^2+b^3=1\\a-b=5\end{cases}}\)
<=> \(\hept{\begin{cases}a=3\\b=-2\end{cases}}\)
<=> x = 10
giai phuong trinh sau:
\(\sqrt{x+3+4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}}=5\)
giai phuong trinh \(\sqrt{8+\sqrt{x-3}}+\sqrt{5-\sqrt{x-3}=5}\)
giai phuong trinh
\(\left(\sqrt{x+5}-\sqrt{x+2}\right)\left(1+\sqrt{x^2+7x+10}\right)=3\)
\(\sqrt{x+1}=\sqrt{5}-3\)giai phuong trinh
Giai phuong trinh :\(\sqrt{2-x^2+2x}+\sqrt{-x^2-6x+8}=1+\sqrt{3}\)
Giai phuong trinh \(x\sqrt{x^2-x+1}+2\sqrt{3x+1}=x^2+x+3\)
Giai phuong trinh : \(2\left(x^2+2\right)=5\sqrt{x^3+1}\)
giai he phuong trinh
\(\hept{\begin{cases}x^2-4\sqrt{3x-2}+10=2y\\y^2-6\sqrt{4y-3}+11=x\end{cases}}\)
Giai phuong trinh
\(\sqrt{x-\sqrt{x-2}}+\sqrt{x+\sqrt{x-2}}=3\)
