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18 tháng 6 2019

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

\(=x^4-2x^3-3x^2+4x+4+x^2-4x+4\)

\(=x^4-2x^3-2x^2+8\)

\(=x^3\left(x-2\right)-2\left(x^2-4\right)\)

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

\(=\left(x-2\right)\left(x^3-2x-4\right)\)

\(=\left(x-2\right)\left[x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)\right]\)

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

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

8 tháng 9 2019

Câu a):

ta có (x2-x-2)2+(x-2)2

=((x-2)2(x+1))2+(x-2)2

=(x-2)2(x2+2x+2)

Y
17 tháng 6 2019

a) \(A=\left(x^2+x-2\right)\left(x+7\right)-16\)

\(=x^3+8x^2+5x-14-16\)

\(=x^3+8x^2+5x-30\)

\(=x^3+3x^2+5x^2+15x-10x-30\)

\(=x^2\left(x+3\right)+5x\left(x+3\right)-10\left(x+3\right)\)

\(=\left(x^2+5x-10\right)\left(x+3\right)\)

b) \(A=x^4-2x^3-3x^2+4x+4+x^2-4x+4\)

\(=x^4-2x^3-2x^2+8\)

\(=x^3\left(x-2\right)-2\left(x^2-4\right)\)

\(=\left(x-2\right)\left(x^3-2x-4\right)\)

\(=\left(x-2\right)\left[x^2\left(x+2\right)+2x\left(x+2\right)-2\left(x+2\right)\right]\)

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

c) \(81x^4+4=81x^4+36x^2+4-36x^2\)

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

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

d) \(\left(x^2-3\right)^2+16=x^4-6x^2+25\)

\(=\left(x^4+10x^2+25\right)-16x^2\)

\(=\left(x^2+5\right)^2-\left(4x\right)^2\)

\(=\left(x^2-4x+5\right)\left(x^2+4x+5\right)\)

Y
17 tháng 6 2019

sửa câu b) xíu nha!

\(A=\left(x-2\right)\left(x^3-2x-4\right)\)

\(=\left(x-2\right)\left[x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)\right]\)

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

NV
17 tháng 6 2019

\(x^4-6x^2+25=x^4+10x^2+25-16x^2\)

\(=\left(x^2+5\right)^2-\left(4x\right)^2=\left(x^2-4x+5\right)\left(x^2+4x+5\right)\)

Y
17 tháng 6 2019

\(=x^4-6x^2+25\)

\(=x^4+10x^2+25-16x^2\)

\(=\left(x^2+5\right)^2-\left(4x\right)^2\)

\(=\left(x^2-4x+5\right)\left(x^2+4x+5\right)\)

21 tháng 6 2019

\(\left(x^2-6x\right)^2-2\left(x-3\right)^2-81=\left[\left(x^2-6x\right)^2-81\right]-2\left(x-3\right)^2=\left[\left(x^2-6x\right)^2-9^2\right]-2\left(x-3\right)^2=\left(x^2-6x+9\right)\left(x^2-6x-9\right)-2\left(x-3\right)^2=\left(x-3\right)^2\left(x^2-6x-9\right)-2\left(x-3\right)^2=\left(x-3\right)^2\left(x^2-6x+11\right)\)

21 tháng 6 2019

=\(\left(x-3\right)^2\left(x^2-6x-11\right)\)

nha

1 tháng 5 2019

1) x2-2xy+y2-x+y
(=) (x-y)2-(x-y)
(=) [(x-y)-1].(x-y)
(=) (x-y-1).(x-y)
C= (x-y)(x2+xy+y2)-x(x2-y)+y(y2-x)
(=) x3-y3-x3+xy+y3-xy

(=)(x3-x3)+(-y3+y3)+(xy-xy)
(=) 0

1 tháng 5 2019

đúng nha

Y
17 tháng 6 2019

a) \(=x^4-2x^3-3x^2+4x+4+x^2-4x+4\)

\(=x^4-2x^3-2x^2+8\)

\(=x^3\left(x-2\right)-2x\left(x-2\right)-4\left(x-2\right)\)

\(=\left(x^3-2x-4\right)\left(x-2\right)\)

\(=\left[x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)\right]\left(x-2\right)\)

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

b) \(=x^4-x+2019\left(x^2+x+1\right)\)

\(=x\left(x^3-1\right)+2019\left(x^2+x+1\right)\)

\(=x\left(x-1\right)\left(x^2+x+1\right)+2019\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+2019\right)\)\

17 tháng 6 2019

c)\(x^4+2x^3+5x^2+4x-5\\=x^4+x^3+x^3-x^2+x^2+5x^2-x+5x-5\\ =x^2\left(x^2+x-1\right)+x\left(x^2+x-1\right)+5\left(x^2+x-1\right)=\left(x^2+x-1\right)\left(x^2+x+5\right)\)

24 tháng 8 2019

Giải giùm em \(\left(x^2+4x+8\right)^2+3x^3+14x^2+24x\) nha

24 tháng 8 2019

\(=\left(a-1\right)\left(a+4\right)\left(a+3\right)\left(a-2\right)-24=\left(a-2\right)\left(a+4\right)\left(a-1\right)\left(a+3\right)-24\)\(=\left(a^2+2a-8\right)\left(a^2+2a-3\right)-24.dat:a^2+2a-8=h\)\(\Rightarrow\left(a^2+2a-8\right)\left(a^2+2a-3\right)-24=h\left(h+5\right)-24=h^2+5h-24=\left(h-3\right)\left(h+8\right)\)\(=\left(a^2+2a-11\right)a\left(a+2\right)\)

Sửa đề: (x-3)(x+5)-(x-2)(x+2)+(x-2)^2+(x+3)^2-2(x-1)(x+1)

\(=x^2+2x-15-x^2+4+x^2-4x+4+\left(x+3\right)^2-2\left(x^2-1\right)\)

\(=x^2-2x-7+x^2+6x+9-2x^2+2\)

=4x+4

11 tháng 3 2018

đkxđ với mọi x

đặt a=x2+x+1

\(\dfrac{a}{a+1}+\dfrac{a+1}{a+2}=\dfrac{7}{6}\)

<=> \(\dfrac{6a\left(a+2\right)}{6\left(a+1\right)\left(a+2\right)}+\dfrac{6\left(a+1\right)^2}{6\left(a+1\right)\left(a+2\right)}=\dfrac{7\left(a+1\right)\left(a+2\right)}{6\left(a+1\right)\left(a+2\right)}\)

=> 6a(a+2) +6(a+1)2 =7(a+1)(a+2)

<=> 6a2+12a +6a2 +12a+6 =a2 +21a+14

<=> 12a2 -a2+24a-21a+6-14=0

<=> 11a2+3a-8=0

<=> 11a2 +11a-8a-8=0

<=> (11a2 +11a)-(8a+8)=0

<=> 11a(a+1)-8(a+1)=0

<=> (a+1)(11a-8)=0

=> a=-1 và a=\(\dfrac{8}{11}\)

thay a=x2+x+1 ta đc

x2+x+1=-1

<=> x2+x+2 =0 (vô nghiệm)

và x2+x+\(\dfrac{3}{11}\) =0(vô nghiệm )

vậy pt trên vô nghiệm

12 tháng 3 2018

c) \(8\left(x+\dfrac{1}{x}\right)^2+4\left(x^2+\dfrac{1}{x^2}\right)^2-4\left(x^2+\dfrac{1}{x^2}\right)\left(x+\dfrac{1}{x}\right)^2=\left(x+4\right)^2\left(2\right)\)ĐKXĐ : x # 0

( 2) <=> \(8\left(x+\dfrac{1}{x}\right)^2+4\left(x^2+\dfrac{1}{x^2}\right)\left[\left(x^2+\dfrac{1}{x^2}\right)-\left(x+\dfrac{1}{x}\right)^2\right]=\left(x+4\right)^2\)

\(< =>8\left(x+\dfrac{1}{x}\right)^2+4\left(x^2+\dfrac{1}{x^2}\right).\left(-2\right)=\left(x+4\right)^2\)

\(< =>8.\left[\left(x+\dfrac{1}{x}\right)^2-x^2-\dfrac{1}{x^2}\right]=\left(x+4\right)^2\)

\(< =>16=\left(x+4\right)^2\)

<=> x2 + 8x = 0

<=> x( x + 8) = 0

<=> x = 0 ( KTM ) hoặc x = - 8 ( TM )

Vậy,....