Question

Tìm GTLN: M= =x^2 + 4x -5

Answer 1

Ta có: \(M=x^2+4x-5\)

\(=x^2+2.x.2+4-9\)

\(=\left(x+2\right)^2-9\)

Vì \(\left(x+2\right)^2\ge0\forall x\)

\(\Rightarrow M\ge-9\forall x\)

Dấu "=" xảy ra khi \(\left(x+2\right)^2=0\)

\(\Leftrightarrow x+2=0\Leftrightarrow x=-2\)

Vậy \(Max_M=-9\Leftrightarrow x=-2.\)

Answer 2

\(M=-x^2+4x-5=-\left(x^2-4x+4\right)-1=-\left(x-2\right)^2-1\)

Ta thấy: \(-\left(x-2\right)^2\le0\forall x\Rightarrow-\left(x-2\right)^2-1\le-1\)

Dấu ''='' xảy ra khi x - 2 = 0 <=> x = 2

Vậy Max_M = -1 <=> x = 2