a: Ta có: \(\sqrt{3x+2}=5\)
\(\Leftrightarrow3x+2=25\)
\(\Leftrightarrow3x=23\)
hay \(x=\dfrac{23}{3}\)
b: Ta có: \(\sqrt{2x-7}=3\)
\(\Leftrightarrow2x-7=9\)
\(\Leftrightarrow2x=16\)
hay x=8
c: Ta có: \(\sqrt{10-4x}=2\)
\(\Leftrightarrow10-4x=4\)
\(\Leftrightarrow4x=6\)
hay \(x=\dfrac{3}{2}\)
d: Ta có: \(\sqrt{x+4}=x-2\)
\(\Leftrightarrow x^2-4x+4=x+4\)
\(\Leftrightarrow x^2-5x=0\)
\(\Leftrightarrow x\left(x-5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(loại\right)\\x=5\left(nhận\right)\end{matrix}\right.\)
e: Ta có: \(\sqrt{2x-5}=4-x\)
\(\Leftrightarrow x^2-8x+16=2x-5\)
\(\Leftrightarrow x^2-10x+21=0\)
\(\Leftrightarrow\left(x-3\right)\left(x-7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\left(nhận\right)\\x=7\left(loại\right)\end{matrix}\right.\)
f: Ta có: \(\sqrt{9-7x}=x+3\)
\(\Leftrightarrow x^2+6x+9=-7x+9\)
\(\Leftrightarrow x^2+13x=0\)
\(\Leftrightarrow x\left(x+13\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(nhận\right)\\x=-13\left(loại\right)\end{matrix}\right.\)
g: Ta có: \(\sqrt{x^2+9}=x+1\)
\(\Leftrightarrow x^2+2x+1-x^2-9=0\)
\(\Leftrightarrow2x=8\)
hay x=4(nhận
h: Ta có: \(\sqrt{x^2-13}=x-1\)
\(\Leftrightarrow x^2-13=x^2-2x+1\)
\(\Leftrightarrow-2x=-14\)
hay x=7(nhận
