18:
a: Ta có: \(A=-x^2+4x+5\)
\(=-\left(x^2-4x-5\right)\)
\(=-\left(x^2-4x+4-9\right)\)
\(=-\left(x-2\right)^2+9\le9\forall x\)
Dấu '=' xảy ra khi x=2
b: Ta có: \(B=-x^2-4y^2+2x-4y+3\)
\(=-\left(x^2-2x+1+4y^2+4y+1-5\right)\)
\(=-\left(x-1\right)^2-\left(2y+1\right)^2+5\le5\forall x,y\)
Dấu '=' xảy ra khi x=1 và \(y=-\dfrac{1}{2}\)
17:
a: Ta có: \(C=x^2+x-2\)
\(=x^2+2\cdot x\cdot\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{9}{4}\)
\(=\left(x+\dfrac{1}{2}\right)^2-\dfrac{9}{4}\ge-\dfrac{9}{4}\forall x\)
Dấu '=' xảy ra khi \(x=-\dfrac{1}{2}\)
b: Ta có: \(D=x^2+x+y^2-6y+5\)
\(=x^2+x+\dfrac{1}{4}+y^2-6y+9-\dfrac{17}{4}\)
\(=\left(x+\dfrac{1}{2}\right)^2+\left(y-3\right)^2-\dfrac{17}{4}\ge-\dfrac{17}{4}\forall x,y\)
Dấu '=' xảy ra khi \(x=-\dfrac{1}{2};y=3\)
