Question

Answer 1

1) \(\sqrt{2x-5}=7\) (ĐK: \(x\ge\dfrac{5}{2}\))

\(\Leftrightarrow2x-5=7^2\)

\(\Leftrightarrow2x-5=49\)

\(\Leftrightarrow2x=49+5\)

\(\Leftrightarrow2x=54\)

\(\Leftrightarrow x=\dfrac{54}{2}\)

\(\Leftrightarrow x=27\left(tm\right)\)

2) \(\sqrt{2x-3}=13\) (ĐK: \(x\ge\dfrac{3}{2}\))

\(\Leftrightarrow2x-3=13^2\)

\(\Leftrightarrow2x-3=169\)

\(\Leftrightarrow2x=169+3\)

\(\Leftrightarrow2x=172\)

\(\Leftrightarrow x=\dfrac{172}{2}\)

\(\Leftrightarrow x=86\left(tm\right)\)

3) \(3+\sqrt{x-2}=4\) (ĐK: \(x\ge2\))

\(\Leftrightarrow\sqrt{x-2}=4-3\)

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

\(\Leftrightarrow x-2=1\)

\(\Leftrightarrow x=1+2\)

\(\Leftrightarrow x=3\left(tm\right)\)

d) \(\sqrt{x^2-7}=2\) (ĐK: \(\left[{}\begin{matrix}x< -\sqrt{7}\\x\ge\sqrt{7}\end{matrix}\right.\))

\(\Leftrightarrow x^2-7=2^2\)

\(\Leftrightarrow x^2-7=4\)

\(\Leftrightarrow x^2=4+7\)

\(\Leftrightarrow x^2=11\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-\sqrt{11}\left(tm\right)\\x=\sqrt{11}\left(tm\right)\end{matrix}\right.\)