Разлож. ** множ. x^4-20x^2+64=0

Question

Разлож. на множ. x^4-20x^2+64=0

Answer 1

X⁴ - 20x² +64=0

y=x²

y² -20y+64=0
D=400-256=144
y₁=(20-12)/2=4
y₂=(20+12)/2=16

y² -20y+64=(y-4)(y-16)
x⁴ -20x² +64=(x² -4)(x² -16)=(x-2)(x+2)(x-4)(x+4)