Question

tìm GTNN của biểu thức A=2x²-2xy-6x+y²+10

Answer 1

`A=2x^2-2xy-6x+y^2+10`

`A=x^2-2xy+y^2+x^2-6x+10`

`A=(x-y)^2+x^2-6x+9+1`

`A=(x-y)^2+(x-3)^2+1`

Vì `(x-y)^2+(x-3)^2>=0=>A>=1`

Dấu "=" xảy ra khi `{(x-y=0),(x-3=0):}<=>x=y=3`

Answer 2

Answer 3

A=\(\left(x^2-2xy+y^2\right)+\left(x^2-6x+9\right)+1=\left(x-y\right)^2+\left(x-3\right)^2+1\ge1\\ \)

dấu= xảy ra khi x=y=3

tick mik nha

Answer 4

Ta có: \(A=2x^2-2xy-6x+y^2+10\)

\(=\left(x^2-2xy+y^2\right)+\left(x^2-6x+9\right)+1\)

\(=\left(x-y\right)^2+\left(x-3\right)^2+1\ge1\forall x,y\)

Dấu '=' xảy ra khi x=y=3

Answer 5

 

A=2x²-2xy-6x+y²+10

  =(x^2 -2xy+y^2)+(x^2-6x+9)+1

  =(x-y)^2+(x-3)^2+1>=1