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4 tháng 8 2018

b,\(\dfrac{4}{9}x^2+4x+9=\left(\dfrac{2}{3}x\right)^2+2.\dfrac{2}{3}x.3+3^2=\left(\dfrac{2}{3}x+3\right)^2\)

c, \(x^3+9x^2+27x+27=x^3+3.x^2.3+3.x.3^2+3^3=\left(x+3\right)^3\)

d, \(\dfrac{1}{8}-\dfrac{3}{4}x+\dfrac{3}{2}x^2-x^3=\left(\dfrac{1}{2}\right)^3-3.\left(\dfrac{1}{2}\right)^2.x+3.\dfrac{1}{2}.x^2-x^3=\left(\dfrac{1}{2}-x\right)^3\)

TK MIK vui

1 tháng 7 2018

1) \(\left(3x-2\right)^2=9x^2-12x+4\)

\(\left(\dfrac{1}{2}x^2+\dfrac{1}{3}\right)^2=\dfrac{1}{4}x^4+\dfrac{1}{3}x^2+\dfrac{1}{9}\)

\(\left(a+b\sqrt{3}\right)^2=a^2+2\sqrt{3}ab+3b^2\)

2) \(4a^2+4a+1=\left(2a+1\right)^2\)

\(9x^2-6x+1=\left(3x-1\right)^2\)

\(\dfrac{1}{4}x^2-\dfrac{1}{3}xy+\dfrac{1}{9}y^2=\left(\dfrac{1}{2}x-\dfrac{1}{3}y\right)^2\)

25 tháng 7 2017

a)\(x^2+4x+4=x^2+2\cdot2\cdot x+2^2=\left(x+2\right)^2\)

b)\(9x^2+42x+49=\left(3x\right)^2+2\cdot3x\cdot7+7^2=\left(3x+7\right)^2\)

c)\(\dfrac{1}{9}-\dfrac{2}{3}y^4+y^8=\left(\dfrac{1}{3}\right)^2-2\cdot\dfrac{1}{3}\cdot y^4+\left(y^4\right)^2=\left(y^4-\dfrac{1}{3}\right)^2\)

25 tháng 7 2017

a) \(x^2+2.2x+2^2\)

\(=\left(x+2\right)^2\)

b)\(\left(3x\right)^2+2.3.7x+7^2\)

\(=\left(3x+7\right)^2\)

c) \(\left(\dfrac{1}{3}\right)^2-2.\dfrac{1}{3}.y^4+\left(y^4\right)^2\)

\(=\left(\dfrac{1}{3}-y^4\right)^2\)

19 tháng 4 2017

a) x2 + 2x + 1 = x2 + 2.x.1+ 12 = ( x + 1)2

b) 9x2 + y2 + 6xy = (3x)2 + 2.3.x.y + y2 = (3x + y)2

c) 25a2 + 4b2 – 20ab = (5a)2 – 2.5.a.2b. + (2b)2 = (5a – 2b)2

Hoặc 25a2 + 4b2 – 20ab = (2b)2 – 2.2b.5a. + (5a)2 = (2b – 5a)2

d) x2 – x + \(\dfrac{1}{4}\) = x2 – 2.x. \(\dfrac{1}{2}\) + ( \(\dfrac{1}{2}\))22 = ( x - \(\dfrac{1}{2}\) )2

Hoặc x2 – x + \(\dfrac{1}{4}\) = \(\dfrac{1}{4}\) - x + x2 = (\(\dfrac{1}{2}\))2 – 2. \(\dfrac{1}{2}\).x + x2 = (\(\dfrac{1}{2}\) - x)2

19 tháng 4 2017

a) x2 + 2x + 1 = x2+ 2 . x . 1 + 12

= (x + 1)2

b) 9x2 + y2+ 6xy = (3x)2 + 2 . 3 . x . y + y2 = (3x + y)2

c) 25a2 + 4b2– 20ab = (5a)2 – 2 . 5a . 2b + (2b)2 = (5a – 2b)2

Hoặc 25a2 + 4b2 – 20ab = (2b)2 – 2 . 2b . 5a + (5a)2 = (2b – 5a)2

d) x2 – x + 1414 = x2 – 2 . x . 1212 + (12)2(12)2= (x−12)2(x−12)2

Hoặc x2 – x + 1414 = 1414 - x + x2 = (12)2(12)2 - 2 . 1212 . x + x2 = (12−x)2



26 tháng 7 2017

a) x2 +4x+4 = ( x + 2 )2

b) 16x2 - 8xy + y2 = ( 4x - y )2

c)9a2 +16b2 - 24ab = ( 3a - 4y ) 2

d) x2 - x + \(\dfrac{1}{4}\)= ( x - \(\dfrac{1}{2}\))2

e) y2 + \(\dfrac{1}{2}y\) + \(\dfrac{1}{16}\) = ( y + \(\dfrac{1}{4}\))2

15 tháng 8 2018

a , \(16x^2+8x+1=\left(4x\right)^2+2.4x.1+1^2=\left(4x+1\right)^2\)

b , \(x^2-x+\dfrac{1}{4}=x^2-2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2=\left(x-\dfrac{1}{2}\right)^2\)

15 tháng 8 2018

a,(4x+1)2 e,\(\left(\dfrac{3}{2}x-\dfrac{2}{5}\right)^2\)

b,(x-\(\dfrac{1}{2}\))2 g,\(\left(xy+1\right)^2\)

c,(\(x+\dfrac{3}{2}\))2 h,\(\left(x+5\right)^2\)

d,\(\left(x-\dfrac{5}{4}\right)^2\) i,\(-\left(x-6\right)^2\)

k,\(-\left(2x+3\right)^2\)

25 tháng 5 2017

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

26 tháng 4 2017

a,(x+3)^2

b,(x+1/2)^2

10 tháng 2 2018

d. ĐKXĐ: x khác 1, x khác 3

\(\dfrac{x+5}{x-1}=\dfrac{x+1}{\left(x-3\right)}-\dfrac{8}{x^2-4x+3}\)

\(\Leftrightarrow\dfrac{\left(x-3\right)\left(x+5\right)}{\left(x-1\right)\left(x-3\right)}=\dfrac{\left(x+1\right)\left(x-1\right)}{\left(x-1\right)\left(x-3\right)}-\dfrac{8}{\left(x-1\right)\left(x-3\right)}\) \(\Leftrightarrow x^2+2x-15=x^2-1-8\)

\(\Leftrightarrow2x-15+1+8=0\)

\(\Leftrightarrow2x-6=0\)

\(\Leftrightarrow x=3\) (loại)

Vậy pt vô nghiệm

26 tháng 7 2018

Những hằng đẳng thức đáng nhớ

14 tháng 8 2018

a) \(9x^2+6x+1=\left(3x+1\right)^2\)

b)\(x^2-x+\frac{1}{4}=\left(x-\frac{1}{2}\right)^2\)

c)\(x^2y^4-2xy^2+1=\left(xy^2-1\right)^2\)

d) \(x^2+\frac{2}{3}x+\frac{1}{9}=\left(x+\frac{1}{3}\right)^2\)

14 tháng 8 2018

a) 9x2 + 6x + 1 = ( 3x + 1 )2

b) x2 - x + 1/4 = ( x - 1/2)2

c) x2 . y4 - 2xy2 + 1 = ( xy2 - 1 ) 2

d) x2 + 2/3x + 1/9 = (x+1/3)2