giải phương trình
a, \(\sqrt{1+x}-\sqrt{8-x}+\sqrt{\left(1+x\right)\left(8-x\right)}=3\)
b, \(\sqrt{3x^2+5x+8}-\sqrt{3x^2+5x+1}=1\)
c, \(2x^2+4x=\sqrt{\dfrac{x+3}{2}}\)
d, \(2\left(x^2-3x+2\right)=3\sqrt{x^3+8}\)
e, \(729x^4+8\sqrt{1-x^2}=36\)
f, \(7x^2-10x+14=5\sqrt{x^4+4}\)
g, \(x^3+3x^2-3\sqrt[3]{3x+5}=1-3x\)
h, \(\sqrt{4-3\sqrt{10-3x}}=x-2\)
i, \(\sqrt{x-1}+\sqrt{x^2-1}=\sqrt{x^2-5x+4}\)
a) \(\sqrt{1+x}-\sqrt{8-x}+\sqrt{\left(1+x\right)\left(8-x\right)}=3\)
đặt t \(=\sqrt{1+x}-\sqrt{8-x}\)
\(\Leftrightarrow t^2=1+x-2\sqrt{\left(1+x\right)\left(8-x\right)}+8-x\)
\(\Leftrightarrow\sqrt{\left(1+x\right)\left(8-x\right)}=\dfrac{9-t^2}{2}\)
pt \(\Rightarrow t+\dfrac{9-t^2}{2}=3\)
\(\Leftrightarrow t^2-2t-3=0\)
\(\Leftrightarrow\left[{}\begin{matrix}t=-1\\t=3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{1+x}-\sqrt{8-x}=-1\\\sqrt{1+x}-\sqrt{8+x}=3\end{matrix}\right.\)
suy ra tìm đc x
câu b đặt t =\(3x^2+5x+8\)
ta có pt \(\Leftrightarrow\sqrt{t}-\sqrt{t-7}=1\)
\(\Rightarrow t=16\)
\(\Leftrightarrow3x^2+5x+8=16\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{8}{3}\end{matrix}\right.\)
