Пусть x1, x2 — корни уравнения 2x^2+3x−4=0. Чему равно значение выражения 16(x1^4+x2^4)?

По теореме Виета x1 + x2 = -b/a = -3/2 x1*x2 = c/a = -4/2 = -2 x1^4 + x2^4 = x1^4 + 2x1^2*x2^2 + x2^4 - 2x1^2*x2^2 = = (x1^2 + x2^2)^2 - 2(x1*x2)^2 = = (x1^2 + 2x1*x2 + x2^2 - 2x1*x2)^2 - 2(x1*x2)^2 = = ((x1 + x2)^2 - 2x1*x2)^2 - 2(x1*x2)^2 = ((-3/2)^2 - 2(-2))^2 - 2(-2)^2 = = (9/4 + 4)^2 - 2*4 = (25/4)^2 - 8 = 625/16 - 128/16 = 497/16 16(x1^4+x2^4) = 16*497/16 = 497