Question

решить уравнение: ((x-2)(x-4))^2+2(x-3)^2-2=0

Answer 1

пусть t=x-3

x-4=t-1; x-2=t+1; ((x-2)(x-4))^2+2(x-3)^2-2= ((t+1)(t-1))^2+2t^2-2=

=((t^2-1))^2+2t^2-2=t^4 -2t^2+1+2t^2-2=t^4-1

t^4-1=0

t=-1; t=1

x=2; x=4