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a, A=2x2+y2-2xy-2x+3
= (x2-2xy+y2)+(2x2-2x+2)+1
=(x-y)2+2(x-1)2+1
vì (x-y)2 ≥0 ∀x,y
(x-1)2 ≥ 0 ∀x
=> (x-y)2+2(x-1)2+1 ≥1 ∀x,y
=> A ≥1
= > GTNN A = 1 khi
x-1=0
=> x=1
x-y=0
=> 1-y=0
=> y=1
vậy GTNN A =1 khi x=y=1
\(C=2\left(x-\frac{5}{4}\right)^2+\frac{7}{8}\ge\frac{7}{8}\Rightarrow C_{min}=\frac{7}{8}\)
\(D=\left(x^2+4xy+4y^2\right)+\left(y^2+y+\frac{1}{4}\right)+\frac{8083}{4}\)
\(D=\left(x+2y\right)^2+\left(y+\frac{1}{2}\right)^2+\frac{8083}{4}\ge\frac{8083}{4}\)
\(E=\frac{1}{2}\left(4x^2+y^2+\frac{9}{4}-4xy-6x+3y\right)+\frac{1}{2}\left(y^2+y+\frac{1}{4}\right)+\frac{15}{4}\)
\(E=\frac{1}{2}\left(2x-y-\frac{3}{2}\right)^2+\frac{1}{2}\left(y+\frac{1}{2}\right)^2+\frac{15}{4}\ge\frac{15}{4}\)
\(A=-\left(x-2\right)^2+11\le11\)
\(B=-\left(x+\frac{1}{2}\right)^2+\frac{9}{4}\le\frac{9}{4}\)
\(C=-\left(x-3y\right)^2-\left(y-2\right)^2+11\le11\)
\(N=x^2+y^2+xy+x+y\)
\(\Rightarrow N=\left(x^2+xy+y^2\right)+\left(x+y\right)\)
\(\Rightarrow N=\left(x+y\right)^2+\left(x+y\right)\)
\(\Rightarrow N=\left(x+y\right)\left(x+y+1\right)\)
(a + b)2 = a2 + 2ab + b2