Toán Lớp 8: Tìm GTNN của P =x^4-2x^3+3x^2-2x+2
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Toán Lớp 8: Tìm GTNN của P =x^4-2x^3+3x^2-2x+2
Comments ( 1 )
P=x^4 – 2x^3 +3x^2-2x+2
=(x^4 – 2x^3+x^2) + (2x^2-2x)+1+1
=(x^2-x)^2 +2(x^2-x).1+1^2+1
=(x^2-x+1)^2+1
=(x^2-2 . x . 1/2+1/4 +3/4)^2+1
=[(x-1/2)^2 +3/4]^2+1>= (3/4)^2+1=25/16 với mọi x
Dấu “=” xảy ra khi : x-1/2=0<=>x=1/2
Vậy min P=25/16<=>x=1/2