Question

1. giải phương trình

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

b. \(\left(7-\sqrt{x}\right)\left(8-\sqrt{x}\right)=x+11\)

c. \(1+\sqrt{3x+1}=3x\)

d. \(\sqrt{\dfrac{3x+7}{x+3}}=4\)

Answer 1

a: =>\(\sqrt{3x-5}+2=x+1\)

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

\(\Leftrightarrow\left\{{}\begin{matrix}x>=1\\x^2-2x+1-3x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=3\end{matrix}\right.\)

b: \(\Leftrightarrow x-15\sqrt{x}+56=x+11\)

=>-15 căn x=-45

=>x=9

c: =>căn 3x+1=3x-1

\(\Leftrightarrow\left\{{}\begin{matrix}x>=\dfrac{1}{3}\\9x^2-6x+1-3x-1=0\end{matrix}\right.\Leftrightarrow x=1\)

d: =>(3x+7)/(x+3)=16

=>16x+48=3x+7

=>13x=-41

=>x=-41/13