Question

  giúp e e,f,g,h với ạ

Answer 1

e: ĐKXĐ: x>=5/4

\(\sqrt{4x-5}=7\)

=>\(4x-5=7^2=49\)

=>4x=49+5=54

=>\(x=\dfrac{54}{4}=13,5\left(nhận\right)\)

f: ĐKXĐ: \(x\in R\)

\(\sqrt{x^2+3x+6}=\sqrt{6}\)

=>\(x^2+3x+6=6\)

=>\(x^2+3x=0\)

=>x(x+3)=0

=>\(\left[{}\begin{matrix}x=0\\x+3=0\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}x=0\\x=-3\end{matrix}\right.\)

g: ĐKXĐ: \(x\in R\)

\(\sqrt{x^2-5x+10}=2\)

=>\(x^2-5x+10=2^2=4\)

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

=>(x-2)(x-3)=0

=>\(\left[{}\begin{matrix}x-2=0\\x-3=0\end{matrix}\right.\)

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

h: ĐKXĐ: \(x^2+3x-4>=0\)

=>(x+4)(x-1)>=0

=>\(\left[{}\begin{matrix}x>=1\\x< =-4\end{matrix}\right.\)

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

=>\(\left\{{}\begin{matrix}x-1>=0\\x^2+3x-4=\left(x-1\right)^2\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x>=1\\x^2+3x-4-x^2+2x-1=0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x>=1\\5x=5\end{matrix}\right.\)

=>x=1