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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
Bài 1:
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) \(4x^2-y^2-12x+2y+8\)
\(=4x^2-12x+9-y^2+2y-1\)
\(=\left(4x^2-12x+9\right)-\left(y^2-2y+1\right)\)
\(=\left(2x-3\right)^2-\left(y-1\right)^2\)
Bài 2:
\(P=4+8x-16x^2\)
\(P=-\left(16x^2-8x+4\right)\)
\(P=-\left[\left(4x\right)^2-2.4x+1+3\right]\)
\(P=-\left(4x-1\right)^2-3\)
Vì \(-\left(4x-1\right)^2\le0\) với mọi x
\(\Rightarrow-\left(4x-1\right)^2-3\le-3\) với mọi x
\(\Rightarrow Pmax=-3\Leftrightarrow4x-1=0\)
\(\Rightarrow4x=1\)
\(\Rightarrow x=\dfrac{1}{4}\)
Vậy Pmax = -3 <=> x = 1/4
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
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) \(4x^2+2z^2-4xz-2z+1\)
\(=4x^2+z^2+z^2-4xz-2z+1\)
\(=\left(4x^2-4xz+z^2\right)+\left(z^2-2z+1\right)\)
\(=\left(2x-z\right)^2+\left(z-1\right)^2\)
1a/ z2 - 6z + 5 - t2 - 4t = z2 - 2 . 3z + 32 - 4 - t2 - 4t = (z2 - 2 . 3z + 32) - (22 + 2 . 2t + t2) = (z - 3)2 - (2 + t)2
b/ x2 - 2xy + 2y2 + 2y2 + 1 = x2 - 2xy + y2 + y2 + 2y + 1 = (x2 - 2xy + y2) + (y2 + 2y + 1) = (x - y)2 + (y + 1)2
c/ 4x2 - 12x - y2 + 2y + 8 = (2x)2 - 12x - y2 + 2y + 32 - 1 = [ (2x)2 - 2 . 3 . 2x + 32 ] - (y2 - 2y + 1) = (2x - 3)2 - (y - 1)2
2a/ (x + y + 4)(x + y - 4) = x2 + xy - 4x + xy + y2 - 4y + 4x + 4y + 16 = x2 + (xy + xy) + (-4x + 4x) + (-4y + 4y) + y2 + 16
= x2 + 2xy + y2 + 42 = (x + y)2 + 42
b/ (x - y + 6)(x + y - 6) = x2 + xy - 6x - xy - y2 + 6y + 6x + 6y - 36 = x2 + (xy - xy) + (-6x + 6x) + (6y + 6y) - y2 - 36
= x2 - y2 + 12y - 62 = x2 - (y2 - 12y + 62) = x2 - (y2 - 2 . 6y + 62) = x2 - (y - 6)2
c/ (y + 2z - 3)(y - 2z - 3) = y2 -2yz - 3y + 2yz - 4z2 - 6z - 3y + 6z + 9 = y2 + (-2yz + 2yz) + (-3y - 3y) + (-6z + 6z) - 4z2 + 9
= y2 - 6y - 4z2 + 9 = (y2 - 6y + 9) - 4z2 = (y - 3)2 - (2z)2
d/ (x + 2y + 3z)(2y + 3z - x) = 2xy + 3xz - x2 + 4y2 + 6yz - 2xy + 6yz + 9z2 - 3xz = (2xy - 2xy) + (3xz - 3xz) - x2 + (6yz + 6yz) + 9z2 + 4y2
= -x2 + 4y2 + 12yz + 9z2 = (4y2 + 12yz + 9z2) - x2 = [ (2y)2 + 2 . 2 . 3yz + (3z)2 ] - x2 = (2y + 3z)2 - x2
a, \(27^2+13^2+2.37.13=\left(27+13\right)^2\)
b, \(87^2+57^2-174.67=\left(87-57\right)^2\)
c, \(x^2-2xy+2y^2+2y+1\)
\(=\left(x^2-2xy+y^2\right)+\left(y^2+2y+1\right)\)
\(=\left(x-y\right)^2+\left(y+1\right)^2\)
d, \(4x^2-12x-y^2+2y+1\)
\(=4\left(x^2-3x\right)-\left(y^2-2y+1\right)+2\)
\(=4\left(x^2-\dfrac{3}{2}.x.2+\dfrac{9}{4}-\dfrac{9}{4}\right)-\left(y-1\right)^2+2\)
\(=\left(x-\dfrac{3}{2}\right)^2-\left(y-1\right)^2-7\)
1) \(4x^2-12x+y^2-4y+13\)
\(=\left(4x^2-12x+9\right)+\left(y^2-4y+4\right)\)
\(=\left[\left(2x\right)^2-2.2x.3+3^2\right]+\left(y^2-2.2y+4\right)\)
\(=\left(2x-3\right)^2+\left(y-2\right)^2\)
2) \(x^2+y^2+2y-6x+10\)
\(=\left(x^2+2y+1\right)+\left(y^2-6x+9\right)\)
\(=\left(x+1\right)^2+\left(y-3\right)^2\)
3) \(4x^2+9y^2-4x+6y+2\)
\(=\left(4x^2-4x+1\right)+\left(9y^2+6y+1\right)\)
\(=\left(2x-1\right)^2+\left(3y+1\right)^2\)
4) \(y^2+2y+5-12x+9x^2\)
\(\left(y^2+2y+1\right)+\left(9x^2-12x+4\right)\)
\(=\left(y+1\right)^2+\left(3x-2\right)^2\)
5) \(x^2+26+6y+9y^2-10x\)
\(=\left(x^2-10x+25\right)+\left(9y^2+6y+1\right)\)
\(=\left(x-5\right)^2+\left(3y+1\right)^2\)
a) \(\Rightarrow\left(x^2+2\times5x+25\right)+\left(y^2+2y+1\right)\)
\(\Rightarrow\left(x+5\right)^2+\left(y+1\right)^2\)
câu d thì s ạ ?