Tenglamaning ildizlari yig‘indisini toping: x² + 1/x² + 2(x + 1/x) − 6 = 0. A) −3; B) −4; C) 1; D) −2.

\(x\neq 0\). Belgilaymiz: \(t=x+\frac1x\). U holda \(x^2+\frac1{x^2}=t^2-2\).

\(t^2-2+2t-6=0\), demak \(t^2+2t-8=0\), ya’ni \((t-2)(t+4)=0\).

\(t=2\) bo‘lsa, \(x=1\). \(t=-4\) bo‘lsa, \(x^2+4x+1=0\), ildizlar yig‘indisi \(-4\).

Shunday qilib, barcha ildizlar yig‘indisi \(1+(-4)=-3\).

Javob: A) −3.