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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
a) \(\Rightarrow\left(x^2+2\times5x+25\right)+\left(y^2+2y+1\right)\)
\(\Rightarrow\left(x+5\right)^2+\left(y+1\right)^2\)
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) \(4x^2+2z^2-4xz-2z+1\)
\(=4x^2+z^2+z^2-4xz-2z+1\)
\(=\left(4x^2-4xz+z^2\right)+\left(z^2-2z+1\right)\)
\(=\left(2x-z\right)^2+\left(z-1\right)^2\)
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
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) \(x^2+26+6y+9y^2-10x\)
\(=\left(x^2-10x+25\right)+\left(9y^2+6y+1\right)\)
\(=\left(x-5\right)^2+\left(3y+1\right)^2\)
Bài 1:
a, \(x^2+10x+26+y^2+2y\)
\(=x^2+2.x.5+5^2+y^2+2.y.1+1^2\)
\(=\left(x+5\right)^2+\left(y+1\right)^2\)
b, \(x^2-2xy+2y^2+2y+1\)
\(=x^2-2.x.y+y^2+y^2+2.y.1+1^2\)
\(=\left(x-y\right)^2+\left(y+1\right)^2\)
c, \(4x^2+2z^2-4xz-2z+1\)
\(=\left(2x\right)^2-2.2x.z+z^2+z^2-2.z.1+1^2\)
\(=\left(2x-z\right)^2+\left(z-1\right)^2\)
Chúc bạn học tốt!!!
Bài1:
Bn kia giải r nhé
Bài 2:
a)\(127^2+146.127+73^2=127^2+2.73.127+73^2\)
=\(\left(127+73\right)^2=200^2=40000\)
b)\(31,8^2-63,6.21,8+21,8^2=\left(31,8-21,8\right)^2=10^2=100\)
c)\(2018^2-2017^2+2016^2-2015^2+...+2^2-1\)
=\(\left(2018+2017\right)+\left(2015+2016\right)+...+\left(2+1\right)\)
=4025+4031+...+3
=...(bn tự tính)
d)\(2017^2-2016.2018=2017^2-\left(2017^2-1\right)=1\)
a) x2+6x+9=x2+2.x.3+32=(x+3)2
b) x2+x+\(\dfrac{1}{4}\)=x2+2.x.\(\dfrac{1}{2}\)+\(\dfrac{1}{4}\)=(x+\(\dfrac{1}{2}\))2
c) 2xy2+x2y4+1=(xy2)2+2.xy2+1=(xy2+1)2
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, \(27^2+13^2+2.37.13=\left(27+13\right)^2\)
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, \(4x^2-12x-y^2+2y+1\)
\(=4\left(x^2-3x\right)-\left(y^2-2y+1\right)+2\)
\(=4\left(x^2-\dfrac{3}{2}.x.2+\dfrac{9}{4}-\dfrac{9}{4}\right)-\left(y-1\right)^2+2\)
\(=\left(x-\dfrac{3}{2}\right)^2-\left(y-1\right)^2-7\)