Verified answer

Дано

[tex]\displaystyle x^2-9x+5=0[/tex]

по т. Виетта

[tex]\displaystyle \left \{ {{x_1+x_2=-p} \atop {x_1*x_2=q}} \right. \\\\\left \{ {{x_1+x_2=9} \atop {x_1*x_2=5}} \right. \\\\x_1^2+x_2^2=(x_1+x_2)^2-2x_1*x_2=9^2-2*5=81-10=71[/tex]