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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 8: tim gtnn cuar 2x^2+3y^2-2xy+4x-7y+2012

Home/ Toán Lớp 8: tim gtnn cuar 2x^2+3y^2-2xy+4x-7y+2012

Toán Lớp 8: tim gtnn cuar 2x^2+3y^2-2xy+4x-7y+2012

Tháng Bảy 6, 2022 Toán học 1 Comment 0 views

Toán Lớp 8: tim gtnn cuar 2x^2+3y^2-2xy+4x-7y+2012

Comments ( 1 )

  1. dantam45
    dantam45
    6 Tháng Bảy, 2022 at 5:07 chiều
    Reply
    #laviken#
    Gọi A=2x^2+3y^2-2xy+4x-7y+2012
    A=2x^2+3y^2-2xy+4x-7y+2012
    2A=2(2x^2+3y^2-2xy+4x-7y+2012)
    2A=4x^2+6y^2-4xy+8x-14y+4024
    =(4x^2-4xy+y^2)+5y^2+8x-14y+4024
    =(2x-y)^2+4(2x-y)+5y^2-10y+4024
    =(2x-y)^2+4(2x-y)+4+5(y^2-y+1)+4015
    =(2x-y+2)^2+5(y-1)^2+4015\ge4015
    =>A\ge4015/2
    Vậy Amin=4015/2 khi (x,y)=((-1)/2,1)

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222-9+11+12:2*14+14 = ? ( )

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