Question

Tìm x

a, \(2x+3-\sqrt{x+1}=4\)

b, \(x^2+\sqrt{x+7}=7\)

c, \(4x-2\sqrt{4x+1}=6\)

Answer 1

a: =>\(\sqrt{x+1}=2x-1\)

=>\(\Leftrightarrow\left\{{}\begin{matrix}x>=\dfrac{1}{2}\\4x^2-4x+1=x+1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>=\dfrac{1}{2}\\x\left(4x-5\right)=0\end{matrix}\right.\)

=>x=5/4

c: \(\Leftrightarrow2\sqrt{4x+1}=4x-6\)

=>\(\sqrt{4x+1}=2x-3\)

\(\Leftrightarrow\left\{{}\begin{matrix}x>=\dfrac{3}{2}\\4x^2-12x+9=4x+1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>=\dfrac{3}{2}\\4x^2-16x+8=0\end{matrix}\right.\)

\(\Leftrightarrow x=2+\sqrt{2}\)