Toán Lớp 8: Tìm x,y:
x^2 + 10y^2 + 6xy – 2x – 7y = -5/4
Leave a reply
Register Now
Login
Lost Password
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Toán Lớp 8: Tìm x,y:
x^2 + 10y^2 + 6xy – 2x – 7y = -5/4
Comments ( 2 )
<=>x^2+10y^2+6xy-2x-7y+5/4=0
<=>x^2+9y^2+y^2+6xy-2x-7y+5/4=0
<=>x^2+(3y)^2+6xy-2x-6y+y^2-y+5/4=0
<=>x^2+(3y)^2+6xy-2x-6y+y^2-y+1+1/4=0
<=>[x^2+(3y)^2+1^2+6xy-2x-6y]+(y^2-y+1/4)=0
<=>[x^2+(3y)^2+1^2+2.x.3y-2.x.1-2.3y.1]+[y^2-2.y . 1/2+(1/2)^2]=0
<=>(x+3y-1)^2+(y-1/2)^2=0
Ta có:
{((x+3y-1)^2ge0forallx;y),((y-1/2)^2ge0forally):}
=>(x+3y-1)^2+(y-1/2)^2ge0forallx;y
Mà (x+3y-1)^2+(y-1/2)^2=0
<=>{((x+3y-1)^2=0),((y-1/2)^2=0):}
<=>{(x+3y-1=0),(y-1/2=0):}
<=>{(x+3y=1),(y=1/2):}
<=>{(x+3/2=1),(y=1/2):}
<=>{(x=-1/2),(y=1/2):}
Vậy x=-1/2;y=1/2
Áp dụng hằng đẳng thức:
(a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc