(x-1)²=(x+2)⁴ ⇔ (x+2)⁴-(x-1)²=0 ⇔ ((x+2)²-(x-1))((x+2)²+(x-1))=0 ⇔ (x²+4x+4-x+1)(x²+4x+4+x-1)=0 ⇔ (x²+3x+5)(x²+5x+3)=0 ⇔ x²+3x+5=0 ∪ x²+5x+3=0
x²+3x+5=0, D=9-20<0 ⇒ x=∅
x²+5x+3=0, D=25-12=13 ⇒ x=(-5±√13)/2
Ответ: x=(-5±√13)/2
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(x-1)²=(x+2)⁴ ⇔ (x+2)⁴-(x-1)²=0 ⇔ ((x+2)²-(x-1))((x+2)²+(x-1))=0 ⇔ (x²+4x+4-x+1)(x²+4x+4+x-1)=0 ⇔ (x²+3x+5)(x²+5x+3)=0 ⇔ x²+3x+5=0 ∪ x²+5x+3=0
x²+3x+5=0, D=9-20<0 ⇒ x=∅
x²+5x+3=0, D=25-12=13 ⇒ x=(-5±√13)/2
Ответ: x=(-5±√13)/2