Question

\(\sqrt{2+\sqrt{3x-5}}=\sqrt{x+1}\) giải pt

Answer 1

Ta có: \(\sqrt{2+\sqrt{3x-5}}=\sqrt{x+1}\)

\(\Leftrightarrow\sqrt{3x-5}+2=x+1\)

\(\Leftrightarrow\sqrt{3x-5}=x-1\)

\(\Leftrightarrow x^2-2x+1-3x+5=0\)

\(\Leftrightarrow x^2-5x+6=0\)

\(\Leftrightarrow\left(x-2\right)\left(x-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=2\left(nhận\right)\\x=3\left(nhận\right)\end{matrix}\right.\)

Answer 2

ĐKXĐ: \(\left\{{}\begin{matrix}2+\sqrt{3x-5}\ge0\\3x-5\ge0\\x+1\ge0\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}\sqrt{3x-5}\ge-2\\x\ge\dfrac{5}{3}\\x\ge-1\end{matrix}\right.\)\(\Rightarrow x\ge\dfrac{5}{3}\)