Tim tât ca cac căp sô x,y thoa man:2010x^2+2011y^2-4020x+4022y+4021=0
Cac ban giup minh nha .Minh cân gâp
Tìm tất cả các số x, y thỏa mãn:
2010x2+2011y2-4020x+4022y+4021=0
Tìm tất cả các cặp số x,y thỏa mãn
\(2010x^2+2011y^2-4020x+4022y+4021=0\)
Ta có:
\(2010x^2+2011y^2-4020x+4022y+4021=0\)
\(\Leftrightarrow(2010x^2-4020x+2010)+(2011y^2+4022y+2011)=0\)
\(\Leftrightarrow2010(x^2-2x+1)+2011(y^2+2y+1)=0\)
\(\Leftrightarrow2010(x-1)^2+2011(y+1)^2=0\)
Ta thấy:
\(\left\{{}\begin{matrix}2010\left(x-1\right)^2\ge0\forall x\\2011\left(y+1\right)^2\ge0\forall y\end{matrix}\right.\)
\(\Rightarrow2010(x-1)^2+2011(y+1)^2\ge0\forall x,y\)
Mà \(\Leftrightarrow2010(x-1)^2+2011(y+1)^2=0\)
\(\Rightarrow\left\{{}\begin{matrix}2010\left(x-1\right)^2=0\\2011\left(y+1\right)^2=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=-1\end{matrix}\right.\)
Vậy \(\left\{{}\begin{matrix}x=1\\y=-1\end{matrix}\right.\)
Tim tat ca cac so nguyen x,y thoa man x^2 + 8y^2 - 6y - 2x + 6y + 6 = 0. ai biet giai giup minh voi,toan nang cao lop 9 do,cam on moi nguoi nhieu
cac ban oi giup minh voi
1.tim a,b thuoc Z,biet:a.(2b-3)=-6
2.cho x,y thuoc Z thoa man x mu 2 +y mu 2 chia het cho 3.chung to x va y chia het cho 3.
so gia tri cua x thoa man x^2+\(\frac{1}{x^2}\) =2
giup minh vs minh se tik cho cac ban nha
x^2 + 1/x^2 \(\ge\)2 ( AM-GM )
Mà x^2 + 1/x^2 = 2
=> x^4 = 1 => x = 1 hoặc -1
gia tri x >0 thoa man x/3/50=2/3/xla x=
(nhap ket qua duoi dang phan so toi gian)
cac ban giup minh nha
Tim bo ba x y z thoa man
X^2+2y^2+2^2-2(xy+2y+2z+8)=0
Giup Minh nha can gap lam
cho pt: x^2-2.(m-2)+m^2=2m-3
Tim m de pt co 2 nghiem phan biet x1,x2 thoa man
\(\frac{1}{x1}+\frac{1}{x2}=\frac{x1+x2}{x}\)
cac ban oi giup minh di minh can gap lam
cho 2 so a,b thoa man : 8.(a2 +b2) =(2a + 2b)2
chung minh rang : a= b .
giup minh bai nay nua nha cac ban ^^
Có: \(8\left(a^2+b^2\right)=\left(2a+2b\right)^2\)
\(\Leftrightarrow8a^2+8b^2=4a^2+8ab+4b^2\)
\(\Leftrightarrow4a^2-8ab+4b^2=0\)
\(\Leftrightarrow a^2-2ab+b^2=0\)
\(\Leftrightarrow\left(a-b\right)^2=0\)
\(\Leftrightarrow a-b=0\Leftrightarrow a=b\)
=> đpcm
8(a2+b2) = (2a + 2b)2
=>8a2+8b2= 4a2 + 8ab + 4b
=> 4a2 + 4b2 = 8ab
=> 4a2 + 4b2 - 8ab = 0
=> (2a - 2b)2 =0
=> 2a - 2b = 0
=> 2(a-b)=0
=>a-b=0
=> a=b