Question

[Ta Sagi]

Giải pt:

1, (x+1)⁴-3(x²+2x)-3=  0

2, \(\frac{2}{\sqrt{5x+1}-1}+\sqrt{5x+1}=\frac{14}{3}\)

Answer 1

[Nyatmax]

2.

\(DK:\hept{\begin{cases}x\ge-\frac{1}{5}\\x\ne0\end{cases}}\)

PT

\(\Leftrightarrow6+3\sqrt{5x+1}\left(\sqrt{5x+1}-1\right)=14\left(\sqrt{5x+1}-1\right)\)

\(\Leftrightarrow15x+23-17\sqrt{5x+1}=0\)

\(\Leftrightarrow\left(68-17\sqrt{5x+1}\right)+\left(15x-45\right)=0\)

\(\Leftrightarrow\frac{17\left(x-3\right)}{4+\sqrt{5x+1}}+15\left(x-3\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(\frac{17}{4+\sqrt{5x+1}}+15\right)=0\)

Vi \(\frac{17}{4+\sqrt{5x+1}}+15>0\)

\(\Rightarrow x=3\left(n\right)\)

Vay nghiem cua PT la \(x=3\)