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1)a)x2+10x+26+y2+2y
=(x2+10x+25)+(y2+2y+1)
=(x+5)2+(y+1)2
b)x2-2xy+2y2+2y+1
=(x2-2xy+y2)+(y2+2y+1)
=(x-y)2+(y+1)2
c)z2-6z+13+t2+4t
=(z2-6z+9)+(t2+4t+4)
=(z-3)2+(t+2)2
d)4x2+2z2-4xz-2z+1
=(4x2-4xz+z2)+(z2-2z+1)
=(2x-z)2+(z-1)2
2)a)(x-3)2-4=0
<=>(x-3-2)(x-3+2)=0
<=>(x-5)(x-1)=0
<=>x-5=0 hoặc x-1=0
<=>x=5 hoặc x=1
b)x2-2x=24
<=>x2-2x-24=0
<=>(x2-6x)+(4x-24)=0
<=>x(x-6)+4(x-6)=0
<=>(x-6)(x+4)=0
<=>x-6=0 hoặc x+4=0
<=>x=6 hoặc x=-4
a) x^2 + 10x + 26 + y^2 + 2y
=x2+10x+25+y2+2y+1
=x2+2.x.5+52+y2+2.y.1+12
=(x+5)2+(y+1)2
b)x^2 - 2xy + 2y^2 + 2y +1
=x2-2xy+y2+y2+2y+1
=(x-y)2+(y+1)2
c)z^2 - 6z + 13 + t^2 + 4t
=z2-6z+9+t2+4z+4
=z2-2.z.3+32+t2+2.t.2+22
=(z-3)2+(t+2)2
d)4x^2 + 2z^2 - 4xz - 2z + 1
=4x2-4xz+z2+z2-2z+1
=(2x)2-2.2x.z+z2+z2-2z.1+12
=(2x-z)2+(z-1)2
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) \(x^2-2xy+2y^2+2y+1\)
\(=\left(x^2-2xy+y^2\right)+\left(y^2+2y+1\right)\)
\(=\left(x-y\right)^2+\left(y+1\right)^2\)
c) \(z^2-6z+13+t^2+4t\)
\(=\left(z^2-6x+9\right)+\left(t^2+4t+4\right)\)
\(=\left(z-3\right)^2+\left(t+2\right)^2\)
d) \(4x^2-2z^2-2xz-2z+1\)
\(=\left(4x^2-4xz+z^2\right)+\left(z^2-2z+1\right)\)
\(=\left(2x-z\right)^2+\left(z-1\right)^2\)
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) \(4x^2+2z^2-4xz-2z+1\)
\(=4x^2+z^2+z^2-4xz-2z+1\)
\(=\left(4x^2-4xz+z^2\right)+\left(z^2-2z+1\right)\)
\(=\left(2x-z\right)^2+\left(z-1\right)^2\)
\(a.\)
\(z^2-6z+5-t^2-4t\)
\(=z^2-6z+9-\left(t^2+4t+4\right)\)
\(=\left(z-3\right)^2-\left(t+2\right)^2\)
\(b.\)
\(4x^2-12x-y^2+2y+1\)
Câu này đề sai sao ấy em !
b, mik nghĩ đề sửa thành: \(4x^2-12x-y^2+2y+8\)
\(=4x^2-12x+9-y^2+2y-1\)
\(=\left(2x\right)^2-2.2.3.x+3^2-\left(y^2-2y+1\right)\)
\(=\left(2x-3\right)^2-\left(y-1\right)^2\)
Lời giải:
a. $x^2+y^2+4y+13-6x$
$=(x^2-6x+9)+(y^2+4y+4)$
$=(x-3)^2+(y+2)^2$
b.
$4x^2-4xy+1+2y^2-2y$
$=(4x^2-4xy+y^2)+(y^2-2y+1)$
$=(2x-y)^2+(y-1)^2$
c.
$x^2-2xy+2y^2+2y+1$
$=(x^2-2xy+y^2)+(y^2+2y+1)$
$=(x-y)^2+(y+1)^2$
a. \(x^2+y^2+4y+12-6x=\left(x^2-6x+9\right)+\left(y^2+4y+4\right)=\left(x-3\right)^2+\left(y+2\right)^2\)b. \(4x^2-4xy+1+2y^2-2y=\left(4x^2-4xy+y^2\right)+\left(y^2-2y+1\right)=\left(2x-y\right)^2+\left(y-1\right)^2\)c. \(x^2-2xy+2y^2+2y+1=\left(x^2-2xy+y^2\right)+\left(y^2+2y+1\right)=\left(x-y\right)^2+\left(y+1\right)^2\)
a) \(\left(x^2-2xy+y^2\right)+\left(y^2+2y+1\right)=\left(x-y\right)^2+\left(y+1\right)^2\)
b) \(\left(z^2-6z+9\right)+\left(t^2+4t+4\right)=\left(z-3\right)^2+\left(t+2\right)^2\)
c) \(\left(4x^2-4xz+z^2\right)+\left(z^2-2z+1\right)=\left(4x-z\right)^2+\left(z-1\right)^2\)
a) x2+10x+26+y2+2y
=x2+10x+25+y2+2y+1
=(x+5)2+(y+1)2
b) z2-6z+5-t2-4t
=z2-6z+9-t2-4t-4
=(z-3)2-(t2+4t+4)
=(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+8
=4x2-12x+9-y2+2y-1
=(2x-3)2-(y2-2y+1)
=(2x-3)2-(y-1)2
x2 + 10x + 26 + y2 + 2y
= x2 + 10 + 25 + 1 + y2 + 2y
= (x2 + 10x + 25) + (y2 + 2y + 1)
= (x + 5)2 + (y + 1)2
x2 - 2xy + 2y2 + 2y + 1
= x2 - 2xy + y2 + y2 + 2y + 1
= (x2 - 2xy + y2) + (y2 + 2y + 1)
= (x - y)2 + (y + 1)2
4x2 + 2z2 - 4xz - 2z + 1
= 4x2 + z2 + z2 - 4xz - 2z + 1
= (4x2 - 4xz + z2) + (z2 - 2z + 1)
= (2x + z)2 + (z - 1)2
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