Ta có:\(A=x^2-4x\)
\(A=x^2-4x+4-4\)
\(A=\left(x-2\right)^2-4\le-4\)
Dấu = xảy ra khi x - 2 = 0 ; x = 2
Vậy Min A = - 4 khi x = 2
Ta có:\(B=x^2+x+1\)
\(B=x^2+2.\frac{1}{2}x+\frac{1}{4}+\frac{3}{4}\)
\(B=\left(x+\frac{1}{2}\right)^2+\frac{3}{4}\ge\frac{3}{4}\)
Dấu = xảy ra khi \(x+\frac{1}{2}=0\Rightarrow x=-\frac{1}{2}\)
Vậy MIn B = 3/4 khi x=-1/2
Ta có:\(C=\left(x+3y-5\right)^2-6xy+26\)
\(C=x^2+9y^2+25+6xy-10x-30y-6xy+26\)
\(C=x^2+9y^2-10x-30y+51\)
\(C=x^2-10x+25+9y^2-30y+25+1\)
\(C=\left(x-5\right)^2+\left(3y-5\right)^2+1\ge1\)
Dấu = xảy ra khi \(x-5=0;3y-5=0\Rightarrow x=5;y=\frac{5}{3}\)
Vậy Min C = 1 khi x=5;y=5/3
C= (x+3y-5)2 - 6xy + 26
= x2 + (3y)2 - 25 - 6xy + 26
= x2 - 6xy + (3y)2 + (-25+26)
= x2 - 2.x.3y + (3y)2 + 1
= (x-3y)2 + 1
Vì (x-3y)2 luôn > hoặc = 0
=) (x-3y)2 + 1 luôn > hoặc = 1
vậy GTNN của C là 1
