Tìm giá trị lớn nhất của A=x²+2x+9
Ta có:
A=x²+2x+9
=x²+2x+1+8
=(x+1)²+8
mà (x+1)²≥0 ∀ x
=>(x+1)²+8≥8 ∀ x hay A≥8 ∀ x
vậy gtln của A là 8 khi và chỉ khi x+1=0 hay x=-1
do đó gtln của A là 8 khi x=-1
Đáp án:
Giải thích các bước giải:
=x² +2x+1+8
với mọi giá trị của x có: (x+1)²≥0
⇒A=(x+1)²+8≥8
dấu "=" xảy ra khi x+1=0⇒x=-1
Vậy min A=8 khi x=-1
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