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22 tháng 8 2018
1. \(x^2-2x+2+4y^2+4y\)
\(=\left(x^2-2x+1\right)+\left(4y^2+4y+1\right)\)
\(=\left(x-1\right)^2+\left(2y+1\right)^2\)
2. \(4x^2-4x+y^2+2y+2\)
\(=\left(4x^2-4x+1\right)+\left(y^2+2y+1\right)\)
\(=\left(2x-1\right)^2+\left(y+1\right)^2\)
3. \(4x^2+4x+4y^2+4y+2\)
\(=\left(4x^2+4x+1\right)+\left(4y^2+4y+1\right)\)
\(=\left(2x+1\right)^2+\left(2y+1\right)^2\)
4. \(4x^2+y^2+12x+4y+13\)
\(=\left(4x^2+12x+9\right)+\left(y^2+4y+4\right)\)
\(=\left(2x+3\right)^2+\left(y+2\right)^2\)
3 tháng 9 2018
\(x^2-2x+2+4y^2+4y\)
\(=\left(x^2-2x+1\right)+\left(4y^2+4y+1\right)\)
\(=\left(x-1\right)^2+\left(2y+1\right)^2\)
\(4x^2-4x+y^2+2y+2\)
\(=\left(2x-1\right)^2+\left(y+1\right)^2\)
DD
2
30 tháng 7 2018
\(a,x^2+y^2-4x-2y+6\)
\(=\left(x^2-4x+4\right)+\left(y^2-2y+1\right)+1\)
\(=\left(x-2\right)^2+\left(y-1\right)^2+1\)
Ta có: \(\left(x-2\right)^2+\left(y-1\right)^2\ge0\forall x,y\)
\(\Rightarrow\left(x-2\right)^2+\left(y-1\right)^2+1\ge1\forall x,y\)
Hay: \(x^2+y^2-4x-2y+6\ge1\)
\(b,x^2+4y^2+z^2-4x+4y-8z+25\)
\(=\left(x^2-4x+4\right)+\left(4y^2+4y+1\right)+\left(z^2-8z+16\right)+4\)
\(=\left(x-2\right)^2+\left(2y+1\right)^2+\left(z-4\right)^2+4\)
Vì: \(\left(x-2\right)^2+\left(2y+1\right)^2+\left(z-4\right)^2\ge0\forall x,y,z\)
\(\Rightarrow\left(x-2\right)^2+\left(2y+1\right)^2+\left(z-4\right)^2+4\ge4\forall x,y,z\)
Hay: \(x^2+4y^2+z^2-4x+4y-8z+25\ge4\)
=.= hok tốt !!
PH
2
XO
18 tháng 7 2021
a) x2 - 7xy - 18y2
= x2 + 2xy - 9xy - 18y2
= x(x + 2y) - 9y(x + 2y)
= (x - 9y)(x + 2y)
b) 4x2 + 8x - 5
= 4x2 - 2x + 10x - 5
= 2x(2x - 1) + 5(2x - 1)
= (2x + 5)(2x - 1)
c) 4x4 - 21x2y2 + y4
= (4x4 + 4x2y2 + y4) -25x2y2
= (2x2 + y2) - (5xy)2
= (2x2 + 5xy + y2)(2x2 - 5xy + y2)
= \(2\left(x^2+\frac{5}{2}xy+\frac{y^2}{2}\right)2\left(x^2-\frac{5}{2}xy+\frac{y^2}{2}\right)\)
= \(4\left[\left(x+\frac{5}{4}y\right)^2-\frac{25}{16}y^2+\frac{y^2}{2}\right]\left[\left(x-\frac{5}{4}\right)y^2-\frac{25}{16}y^2+\frac{y^2}{2}\right]\)
\(=4\left(x+\frac{5}{4}y-\frac{\sqrt{17}}{4}y\right)\left(x+\frac{5}{4}y+\frac{\sqrt{17}}{4}y\right)\left(x-\frac{5}{4}y-\frac{\sqrt{17}y}{4}\right)\left(x-\frac{5}{4}y+\frac{\sqrt{17y}}{4}\right)\)
20 tháng 7 2018
a) 1/2(x3+8)=1/2(x+2)(x2-2x+4)
b) x4(x-y)+2x3(x-y)=x3(x+2)(x-y)
c) x2-(y2-6y+9)=x2-(y-3)2=(x-y+3)(x+y-3)
d) xy(x3+y3)=xy(x+y)(x2-xy+y2)
e)3x2(x2-25y2)=3x2(x-5y)(x+5y)
f) 4x4+4x2y2+y4-4x2y2= (2x2+y2)2-(2xy)2=(2x2-2xy+y2)(2x2+2xy+y2)
20 tháng 7 2018
a) \(\frac{1}{2}x^3+4=\frac{1}{2}\left(x^3+8\right)=\frac{1}{2}\left(x+2\right)\left(x^2-2x+4\right)\)
b) \(x^5-x^4y+2x^4-2x^3y=x^3\left(x^2-xy+2x-2y\right)=x^3\left[x\left(x-y\right)+2\left(x-y\right)\right]=x^2\left(x-y\right)\left(x+2\right)\)
c) \(x^2-y^2+6y-9=x^2-\left(y-3\right)^2=\left(x+y-3\right)\left(x-y+3\right)\)
d) \(x^4y+xy^4=xy\left(x^3+y^3\right)=xy\left(x+y\right)\left(x^2-xy+y^2\right)\)
e) \(3x^4-75x^2y^2=3x^2\left(x^2-25y^2\right)=3x^2\left(x+5y\right)\left(x-5y\right)\).
f) \(4x^4+y^4=\left(2x^2+y^2\right)^2-\left(2xy\right)^2=\left(2x^2+y^2+2xy\right)\left(2x^2-y^2-2xy\right)\)
H9
HT.Phong (9A5)
CTVHS
30 tháng 7 2023
1) \(4x^5y^2-8x^4y^2+4x^3y^2\)
\(=4x^3y^2\left(x^2-2x+1\right)\)
\(=4x^3y^2\left(x^2-2\cdot x\cdot1+1^2\right)\)
\(=4x^3y^2\left(x-1\right)^2\)
2) \(5x^4y^2-10x^3y^2+5x^2y^2\)
\(=5x^2y^2\left(x^2-2x+1\right)\)
\(=5x^2y^2\left(x^2-2\cdot x\cdot1+1^2\right)\)
\(=5x^2y^2\left(x-1\right)^2\)
3) \(12x^2-12xy+3y^2\)
\(=3\left(4x^2-4xy+y^2\right)\)
\(=3\left[\left(2x\right)^2-2\cdot2x\cdot y+y^2\right]\)
\(=3\left(2x-y\right)^2\)
4) \(8x^3-8x^2y+2xy^2\)
\(=2x\left(4x^2-4xy+y^2\right)\)
\(=2x\left[\left(2x\right)^2-2\cdot2x\cdot y+y^2\right]\)
\(=2x\left(2x-y\right)^2\)
5) \(20x^4y^2-20x^3y^3+5x^2y^4\)
\(=5x^2y^2\left(4x^2-4xy+y^2\right)\)
\(=5x^2y^2\left[\left(2x\right)^2-2\cdot2x\cdot y+y^2\right]\)
\(=5x^2y^2\left(2x-y\right)^2\)
29 tháng 7 2023
1: 4x^5y^2-8x^4y^2+4x^3y^2
=4x^3y^2(x^2-2x+1)
=4x^3y^2(x-1)^2
2: \(=5x^2y^2\left(x^2-2x+1\right)=5x^2y^2\left(x-1\right)^2\)
3: \(=3\left(4x^2-4xy+y^2\right)=3\left(2x-y\right)^2\)
4: \(=2x\left(4x^2-4xy+y^2\right)=2x\left(2x-y\right)^2\)
5: \(=5x^2y^2\left(4x^2-4xy+y^2\right)=5x^2y^2\left(2x-y\right)^2\)
H
1
27 tháng 2 2022
\(A=\dfrac{6x^2+21x+22}{x^2+4x+4}\)
\(=\dfrac{6\left(x^2+4x+4\right)-3x-2}{x^2+4x+4}\)
\(=6+\dfrac{-3x-2}{\left(x+2\right)^2}\)
\(=6+\dfrac{-3\left(x+2\right)+4}{\left(x+2\right)^2}\)
\(=6-\dfrac{3}{x+2}+\dfrac{4}{\left(x+2\right)^2}\)
-Đặt \(a=\dfrac{1}{x+2}\) thì:
\(A=6-3a+4a^2=\left(2a\right)^2-2.2a.\dfrac{3}{4}+\dfrac{9}{16}+\dfrac{87}{16}=\left(2a-\dfrac{3}{4}\right)^2+\dfrac{87}{16}\ge\dfrac{87}{16}\)
\(A_{min}=\dfrac{87}{16}\)\(\Leftrightarrow\left(2a-\dfrac{3}{4}\right)^2=0\Leftrightarrow2a-\dfrac{3}{4}=0\Leftrightarrow2a=\dfrac{3}{4}\)
\(\Leftrightarrow2.\dfrac{1}{x+2}=\dfrac{3}{4}\Leftrightarrow\dfrac{1}{x+2}=\dfrac{3}{8}\Leftrightarrow x+2=\dfrac{8}{3}\Leftrightarrow x=\dfrac{2}{3}\)
T
28 tháng 7 2018
1.
\(\frac{25x^4y^3-15x^3y^5+20x^2y^4}{5x^2y^3}\)
\(=\frac{5x^2y^3\left(5x^2-3xy^2+4y\right)}{5x^2y^3}\)
\(=5x^2-3xy^2+4y\)
2.
a) \(27x^4-8x=x\left(27x^3-8\right)\)
\(=x\left(3x-2\right)\left(9x^2+6x+4\right)\)
b) \(16x^2y-4xy^2-4x^3+x^2y\)
\(=4xy\left(4x-y\right)-x^2\left(4x-y\right)\)
\(=x\left(4x-y\right)\left(4y-x\right)\)
c) \(x^2-2x-5+2\sqrt{5}\)
\(=\left(x-1\right)^2-6+2\sqrt{5}\)
\(=\left(x-1\right)^2-\left(6-2\sqrt{5}\right)=\left(x-1\right)^2-\left(\sqrt{5}-1\right)^2\)
\(=\left(x-\sqrt{5}\right)\left(x-2+\sqrt{5}\right)\)
28 tháng 7 2018
Bài 1:
\(\left(25x^4y^3-15x^3y^5+20x^2y^4\right):\left(5x^2y^3\right)\)
\(=\frac{25x^4y^3-15x^3y^5+20x^2y^4}{5x^2y^3}\)
\(=\frac{5x^2y^3\left(5x^2-3xy^2+4y\right)}{5x^2y^3}\)
\(=5x^2-3xy^2+4y\)
Bài 2:
a) \(27x^4-8x\)
\(=x\left(3x-2\right)\left(3^2x^2+2.3x+2^2\right)\)
\(=x\left(3x-2\right)\left(9x^2+6x+4\right)\)
b) \(16x^2y-4xy^2-4x^3+x^2y\)
\(=4y^2+x^2-\left(4x^2\right)^2\)
\(=x\left(-4x^2+xy+4y^2\right)\)
VT
2
20 tháng 7 2016
\(=4x^4+21x^2y^2+y^4-25x^2y^2\)
\(\left(2x^2+y^2\right)-\left(5xy\right)^2\)
\(\left(2x^2+y^2-5xy\right)\left(2x^2+y^2+5xy\right)\)
\(4x^4-21x^2y^2+4y^2=\left(2x^2\right)^2-2.2x^2.2y^2+\left(2y^2\right)^2-13x^2y^2\)
\(=\left(2x^2-2y^2\right)^2-\left(\sqrt{13}xy\right)^2\)
\(=\left(2x^2-\sqrt{13}xy-2y^2\right)\left(2x^2+\sqrt{13}xy-2y^2\right)\)