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1)
\(=x^2-4x+4+y^2+2y+1\)
\(=\left(x-2\right)^2+\left(y+1\right)^2\)
2)
\(=a^2+2ab+b^2+a^2-2ax+x^2\)
\(=\left(a+b\right)^2+\left(a-x\right)^2\)
3)
\(=x^2-2x+1+y^2+6y+9\)
\(=\left(x-1\right)^2+\left(y+3\right)^2\)
4)
\(=x^2-2xy+y^2+x^2+10x+25\)
\(=\left(x-y\right)^2+\left(x+5\right)^2\)
5)
\(=a^2+2ab+b^2+4b^2+4b+1\)
\(=\left(a+b\right)^2+\left(2b+1\right)^2\)
1/ x2 - 4x + 5 + y2 + 2y
= ( x2 - 4x + 4 ) + ( y2 + 2y + 1 )
= ( x - 2 )2 + ( y + 1 )2
2/ 2a2 + 2ab - 2ax + x2 + b2
= ( a2 + 2ab + b2 ) + ( x2 - 2ax + a2 )
= ( a + b )2 + ( x - a )2
3/ x2 - 2x + y2 + 6y + 10
= ( x2 - 2x + 1 ) + ( y2 + 6y + 9 )
= ( x - 1 )2 + ( y + 3 )2
4/ 2x2 + y2 - 2xy + 10x + 25
= ( x2 - 2xy + y2 ) + ( x2 + 10x + 25 )
= ( x - y )2 + ( x + 5 )2
5/ a2 + 2ab + 5b2 + 4b + 1
= ( a2 + 2ab + b2 ) + ( 4b2 + 4b + 1 )
= ( a + b )2 + ( 2b + 1 )2
a) \(x^2-4x+5+y^2+2y=\left(x^2-4x+4\right)+\left(y^2+2y+1\right)\)
\(=\left(x-2\right)^2+\left(y+1\right)^2\)
b) \(2x^2+y^2-2xy+10x+25=\left(x^2+10x+25\right)+\left(x^2-2xy+y^2\right)\)
\(=\left(x+5\right)^2+\left(x-y\right)^2\)
c) \(2x^2+2y^2=\left(x^2-2xy+y^2\right)+\left(x^2+2xy+y^2\right)=\left(x-y\right)^2+\left(x+y\right)^2\)
......................?
mik ko biết
mong bn thông cảm
nha ................
a) \(x^2+10x+26+y^2+2y\)
\(=\left(x^2+10x+25\right)+\left(y^2+2y+1\right)\)
\(=\left(x+5\right)^2+\left(y+1\right)^2\)
b) \(x^2-2xy+2y^2+2y+1=\left(x-y\right)^2+\left(y+1\right)^2\)
thay 2014 = x + 1
sau đó biến đổi rút gọn
a) \(x^2+10x+26+y^2+2y\)
\(=\left(x^2+10x+25\right)+\left(1+2y+y^2\right)\)
\(=\left(x+5\right)^2+\left(1+y\right)^2\)
b) \(x^2-2xy+2y^2+2y+1\)
\(=\left(x^2-2xy+y^2\right)+\left(y^2+2y+1\right)\)
\(=\left(x-y\right)^2+\left(y+1\right)^2\)
c) \(2x^2+2y^2=2\left(x^2+y^2\right)\)
a) \(\Rightarrow\left(x^2+2\times5x+25\right)+\left(y^2+2y+1\right)\)
\(\Rightarrow\left(x+5\right)^2+\left(y+1\right)^2\)
\(1,a,A=x^2-6x+25\)
\(=x^2-2.x.3+9-9+25\)
\(=\left(x-3\right)^2+16\)
Ta có :
\(\left(x-3\right)^2\ge0\)Với mọi x
\(\Rightarrow\left(x-3\right)^2+16\ge16\)
Hay \(A\ge16\)
\(\Rightarrow A_{min}=16\)
\(\Leftrightarrow x=3\)
bài 1:
a) x2 + 10x + 26 + y2 + 2y
= (x2 + 10x + 25) + (y2 + 2y + 1)
= (x + 5)2 + (y + 1)2
b) z2 - 6z + 5 - t2 - 4t
= (z - 3)2 - (t + 2)2
c) x2 - 2xy + 2y2 + 2y + 1
= (x2 - 2xy + y2) + (y2 + 2y + 1)
= (x - y)2 + (y + 1)2
d) 4x2 - 12x - y2 + 2y + 1
= (4x2 - 12x ) - (y2 + 2y + 1)
= ......................................
ok mk nhé!! 4545454654654765765767587876968345232513546546575675767867876876877687975675
a) \(x^2+10x+26+y^2+2y\)
\(=x^2+2.5x+25+1+y^2+2y\)
\(=\left(x^2+2.5x+25\right)+\left(1+2y+y^2\right)\)
\(=\left(x+5\right)^2+\left(1+y\right)^2\)
b) \(x^2-2xy+2y^2+2y+1\)
\(=x^2-2xy+y^2+y^2+2y+1\)
\(=\left(x^2-2xy+y^2\right)+\left(y^2+2y+1\right)\)
\(=\left(x-y\right)^2+\left(y+1\right)^2\)
c) \(z^2-6z+13+t^2+4t\)
\(=z^2-2.3z+9+4+t^2+4t\)
\(=\left(z^2-2.3x+9\right)+\left(4+4t+t^2\right)\)
\(=\left(z-3\right)^2+\left(2+t\right)^2\)
d) \(4x^2+2z^2-4xz-2z+1\)
\(=4x^2+z^2+z^2-4xz-2z+1\)
\(=\left(4x^2-4xz+z^2\right)+\left(z^2-2z+1\right)\)
\(=\left(2x-z\right)^2+\left(z-1\right)^2\)