x1 + x2 = a + 3
x1 * x2 = 2a + 3
(x1 + x2)^2 = x1^2 + 2 * x1 * x2 + x2^2
x1^2 + x2^2 = (x1 + x2)^2 - 2 * x1 * x2
x1^2 + x2^2 = (a + 3)^2 - 2 * (2a + 3) = a^2 + 6a + 9 -4a - 6= a^2 +2a + 3
х1^2+х2^2<3(х1+х2+2)
a^2 +2a + 3 < 3(a + 5)
a^2 - a - 12 < 0
(a - 4)(a + 3) < 0
методом интервалов получаем
-3 < a < 4
ответ: (-3; 4).
x1 + x2 = a + 3
x1 * x2 = 2a + 3
(x1 + x2)^2 = x1^2 + 2 * x1 * x2 + x2^2
x1^2 + x2^2 = (x1 + x2)^2 - 2 * x1 * x2
x1^2 + x2^2 = (a + 3)^2 - 2 * (2a + 3) = a^2 + 6a + 9 -4a - 6= a^2 +2a + 3
х1^2+х2^2<3(х1+х2+2)
a^2 +2a + 3 < 3(a + 5)
a^2 - a - 12 < 0
(a - 4)(a + 3) < 0
методом интервалов получаем
-3 < a < 4
ответ: (-3; 4).