Toán Lớp 8: Tìm gtnn,gtln
x²+3x+9
Hạn 9h
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Toán Lớp 8: Tìm gtnn,gtln
x²+3x+9
Hạn 9h
Comments ( 2 )
=x^2+2.x . 3/2+(3/2)^2+27/4
=(x+3/2)^2+27/4
Ta có:
(x+3/2)^2ge0forallx
=>(x+3/2)^2+27/4ge27/4
=>x^2+3x+9ge27/4
Dấu = xảy ra khi:
(x+3/2)^2=0
<=>x+3/2=0
<=>x=-3/2
Vậy GTNN của x^2+3x+9=27/4 khi và chỉ khi x=-3/2
Ta có:
⇒ (x-3/2)^2 + {27}/4 \ge {27}/4 ∀ x
⇒ A_{min} = {27}/4. Dấu “=” xảy ra khi: