Question

Sa se rezolve in Z ecuatia: 4|3x+2|-√9x²+12x+4(toata sub radical)=21

Answer 1

$4|3x+2|- \sqrt{9 x^{2} +12x+4} =21\Leftrightarrow \\\Leftrightarrow 4|3x+2|- \sqrt{(3x+2) ^{2} } =21\Leftrightarrow \\\Leftrightarrow4|3x+2|-|3x+2|=21\Leftrightarrow \\ \Leftrightarrow3|3x+2|=21\Rightarrow|3x+2}|=7 .$

$Cazul~I:~3x+2=7 \Rightarrow3x=5 \Rightarrowx= \frac{5}{3}\notin Z. \\ Cazul~II:~3x+2=-7 \Rightarrow3x= -9\Rightarrow \boxed{x=-3}.$

$Solutie:~\boxed{x=-3}.$