Question

Tìm Max

a, -x² -x +2

b, -4x² -5x +1

c, -9x² + 24x +6

d, -2x² +x +3

Answer 1

a)\(-x^2-x+2\)

\(=-\left(x^2+x-2\right)\)

\(=-\left(x^2+x+\frac{1}{4}-\frac{7}{4}\right)\)

\(=-\left(x+\frac{1}{2}\right)^2+\frac{7}{4}\le\frac{7}{4}.Với\forall x\in Z\)

Dấu "="  xảy ra khi 

\(x+\frac{1}{2}=0\Leftrightarrow x=-\frac{1}{2}\)

Vậy Max = 7/4 <=> x = -1/2

Answer 2

a, \(-\left(x^2+x\right)+2\)

=\(-\left(x^2+2\cdot\frac{1}{2}x+\frac{1}{4}-\frac{1}{4}\right)+2\)

=\(-\left(x+\frac{1}{2}\right)^2+\frac{9}{4}\le\frac{9}{4}\)

Dấu = xảy ra khi : \(x+\frac{1}{2}=0\)

=> \(x=-\frac{1}{2}\) 

Vậy Max=9/4 khi x=-1/2 

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