Question

\(\sqrt{-x^2+7x+6}=3+2x\)

Answer 1

ĐKXĐ: \(-x^2+7x+6>=0\)

=>\(x^2-7x-6< =0\)

=>\(\dfrac{7-\sqrt{73}}{2}< =x< =\dfrac{7+\sqrt{73}}{2}\)

\(\sqrt{-x^2+7x+6}=3+2x\)

=>\(\left\{{}\begin{matrix}2x+3>=0\\\left(2x+3\right)^2=-x^2+7x+6\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x>=-\dfrac{3}{2}\\4x^2+12x+9+x^2-7x-6=0\end{matrix}\right.\)

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

=>\(x\in\varnothing\)