Question

$(x-1) ^{4} -x ^{2} +2x-73=0$

Answer 1

(x-1)⁴-x²+2x-73=0
(x-1)⁴-(x²-2x+1)-72=0
(x-1)⁴-(x-1)²-72=0
Пусть (x-1)²=t>0   ⇒
t²-t-72=0    D=289
t₁=-8∉    
t₂=9
(x-1)²=9
(x-1)²-3²=0
(x-1+3)*(x-1-3)=0
(x+2)*(x-4)=0
x+2=0   x₁=-2   
x-4=0    x₂=4.
Ответ: x₁=-2     x₂=4.