Question

tìm GTNN

P=5x²+2y²-2xy-4x+2y+2013

Q=5x²+2y²-2xy-4x+2y+3

Answer 1

       \(P=5x^2+2y^2-2xy-4x+2y+2013\)

\(\Leftrightarrow P=\left(x^2-2xy+y^2\right)+\left(4x^2-4x+1\right)+\left(y^2+2y+1\right)+2011\)

\(\Leftrightarrow P=\left(x-y\right)^2+\left(2x-1\right)^2+\left(y+1\right)^2+2011\ge2011\)

\(\Leftrightarrow min_P=2011\)

tương tự ta có : 

\(\Leftrightarrow Q=\left(x^2-2xy+y^2\right)+\left(4x^2-4x+1\right)+\left(y^2+2y+1\right)+1\)

\(\Leftrightarrow Q=\left(x-y\right)^2+\left(2x-1\right)^2+\left(y+1\right)^2+1\ge1\)

\(\Leftrightarrow min_Q=1\)

TK NKA !!!

Answer 2

nỗi ám ảnh của thiếu nhi khi hallowen là đây

Answer 3

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Answer 4

BIỂU TÌNH