Розяжите уравнение (х-4) (х-5) (х-6) (х-7) = 1680

(x-4) (x-7) * (x-5) (x-6) = 1680

(х²-11x+28) * (x²-11x+30) = 1680

х²-11x+28 = t

t * (t+2) = 1680

t² + 2t - 1680 = 0

D=4+4*1680 = 4*1681 = (2*41) ²

t₁; ₂ = (-2+-82) / 2 = - 1+-41

t₁ = - 42 t₂ = 40

х²-11x+28 = - 42 х²-11x+28 = 40

х²-11x+70 = 0 х²-11x-12 = 0

D=121-280<0 корней нет.

х₁ = - 1 х₂ = 12