Question

X为有理数,求X^2-4X^3+10X^2-12X+9的最小值.

Answer 1

x^4-4x^3+10x^2-12x+9

=(x^4-4x^3+6x^2-4x+1)+(4x^2-8x+4)+4

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

因为(x-1)^2≥0

所以(x-1)^2+2≥2

所以[(x-1)^2+2]^2≥4

X^4-4X^3+10X^2-12X+9的最小值是4