\(\sqrt{9x^2+18}+2\sqrt{x^2+2}-\sqrt{25x^2+50}+3=0\)
\(\Leftrightarrow\sqrt{9\left(x^2+2\right)}+2\sqrt{x^2+2}-\sqrt{25\left(x^2+2\right)}+3=0\)
\(\Leftrightarrow3\sqrt{x^2+2}+2\sqrt{x^2+2}-5\sqrt{x^2+2}=-3\)
\(\Leftrightarrow0.\sqrt{x^2+2}=-3\)
\(\Leftrightarrow0=-3\)( vô lý)
Vậy pt vô nghiệm
Đặt \(\sqrt{x^2+2}=a\). Ta có:
\(\sqrt{9x^2+18}+2a-\sqrt{25x^2+50}+3=0\)
\(\Rightarrow\sqrt{9\left(x^2+2\right)}+2a-\sqrt{25\left(x^2+2\right)}+3=0\)
\(\Rightarrow3a+2a-5a+3=0\)
\(\Rightarrow0=-3\) (vô lí)
Vậy phương trình vô nghiệm
√9x2+18+2√x2+2−√25x2+50+3=09x2+18+2x2+2−25x2+50+3=0
⇔√9(x2+2)+2√x2+2−√25(x2+2)+3=0⇔9(x2+2)+2x2+2−25(x2+2)+3=0
⇔3√x2+2+2√x2+2−5√x2+2=−3⇔3x2+2+2x2+2−5x2+2=−3
⇔0.√x2+2=−3⇔0.x2+2=−3
⇔0=−3⇔0=−3( vô lý)
