Đáp án:
\(S = \left\{ {3; - {9 \over 2}} \right\}.\)
Giải thích các bước giải:
\(\eqalign{
& 2{x^2} + 3x - 3 + \sqrt {2{x^2} + 3x + 9} = 30 \cr
& \Leftrightarrow 2{x^2} + 3x + 9 + \sqrt {2{x^2} + 3x + 9} - 12 = 30 \cr
& \Leftrightarrow 2{x^2} + 3x + 9 + \sqrt {2{x^2} + 3x + 9} - 42 = 0 \cr
& Dat\,\,t = \sqrt {2{x^2} + 3x + 9} \,\,\,\left( {t \ge 0} \right) \cr
& Pt:\,\,{t^2} + t - 42 = 0 \Leftrightarrow \left[ \matrix{
t = 6\,\,\,\,\,\left( {tm} \right) \hfill \cr
t = - 7\,\,\left( {ktm} \right) \hfill \cr} \right. \cr
& t = 6 \Rightarrow \sqrt {2{x^2} + 3x + 9} = 6 \cr
& \Leftrightarrow 2{x^2} + 3x + 9 = 36 \cr
& \Leftrightarrow 2{x^2} + 3x - 27 = 0 \cr
& \Leftrightarrow \left[ \matrix{
x = 3 \hfill \cr
x = - {9 \over 2} \hfill \cr} \right. \cr
& \Rightarrow S = \left\{ {3; - {9 \over 2}} \right\}. \cr} \)
