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30 tháng 8 2019

Đặt A=(x + 2) (x + 3) (x + 4) (x + 5) - 24
= (x + 2) (x + 5) (x + 3) (x + 4) - 24
=(x2+7x+10)(x2+7x+12)−24
Đặt a=x2+7x+11 thay vào A ta được :
A=(a-1)(a+1)=a^2-25 = a^2 - 5^2 = (a-5)(a+5) ( 2)
Thế a vào (2) ta được :
A=(x2+7x+11−5)(x2+7x+11+5)

30 tháng 8 2019

(x+1)(x+2)(x+3)(x+4)−24
=[(x+1)\(^2\)+3(x+1)][x\(^2\)+5x+6]−24

=[(x+1)\(^2\)+3(x+1)][(x+1)\(^2\)+3x+5]−24

=[(x+1)\(^2\)+3(x+1)][(x+1)\(^2\)+3(x+1)+2]−24

=[(x+1)\(^2\)+3(x+1)]\(^2\)+2[(x+1)\(^2\)+3(x+1)]\(^2\)−24

=[(x+1)\(^2\)+3(x+1)+1]\(^2\)−25

=[(x+1)\(^2\)+3(x+1)−4][(x+1)\(^2\)+3(x+1)+6]

=(x\(^2\)+5x)(x\(^2\)+5x+10)

23 tháng 9 2016

a) x3 + (a+b+c)x2+ (ab+ac+bc)x +abc

= x3 +ax2+bx2+cx2+abx+acx+bcx+abc

=x3+cx2+abx+abc+ax2+acx+bx2+bcx

=x2 (x+c) + ab (x+c) +ax (x+c) +bx (x+c)

= (x+c) (x2+ab+ax+bx)

= (x+c) { x(x+b)+a(x+b)}

=(x+c) (x+b) (x+a)

3 tháng 11 2019

Ta có:

(x + 2)(x + 3)(x + 4)(x + 5) - 24

= [(x + 2)(x + 5)][(x + 3)(x + 4)] - 24

= (x2 + 5x + 2x + 10)(x2 + 4x + 3x + 12) - 24

= (x2 + 7x + 10)(x2 + 7x + 12) - 24

Đặt x2 + 7x + 10 = k 

=> k(k + 2) - 24 = k2 + 2k - 24 = k2 + 6x - 4x - 24 

                            = k(k + 6)  - 4(k  + 6)

                          = (k - 4)(k + 6)

=> (x + 2)(x + 3)(x + 4)(x + 5) - 24

= (x2 + 7x + 10 - 4)(x2 + 7x + 10 + 6)

= (x2 + 7x + 6)(x2 + 7x + 16)

3 tháng 11 2019

\(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)

\(=\left[\left(x+2\right)\left(x+5\right)\right]\left[\left(x+3\right)\left(x+4\right)\right]-24\)

\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)(1)

Đặt \(x^2+7x+11=t\)thay vào (1) ta được:
\(\left(t-1\right)\left(t+1\right)-24\)

\(=t^2-1-24\)

\(=t^2-25\)

\(=\left(t-5\right)\left(t+5\right)\)Thay \(t=x^2+7x+11\)ta được:

\(\left(x^2+7x+11-5\right)\left(x^2+7x+11+5\right)\)

\(=\left(x^2+7x+6\right)\left(x^2+7x+16\right)\)

\(=\left(x^2+x+6x+6\right)\left(x^2+7x+16\right)\)

\(=\left[x\left(x+1\right)+6\left(x+1\right)\right]\left(x^2+7x+16\right)\)

\(=\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)

25 tháng 2 2017

\(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)

\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)

Let \(t=x^2+7x+10\) we have:

\(=t\left(t+2\right)-24=t^2+2t-24\)

\(=\left(t-4\right)\left(t+6\right)=\left(x^2+7x+10-4\right)\left(x^2+7x+10+6\right)\)

\(=\left(x^2+7x+6\right)\left(x^2+7x+16\right)\)

\(=\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)

(x+2).(x+3).(x+4).(x+5)−24

=(x2+7x+10).(x2+7x+12)−24

=(x2+7x+10).(x2+7x+10+2)−24

Đặt x2+7x+10=t, ta có

t.(t+2)−24

=t2+2t−24

=t2+2t+1−25

=(t−1)2−25

=(t−1−5)(t−1+5)

=(t−6)(t+4)

=(x2+7x+10−6)(x2+7x+10+4)

(x2+7x+4)(x2+7x+14)

P/s tham khảo nha

\(\left(x+2\right).\left(x+3\right).\left(x+4\right).\left(x+5\right)-24\)

\(\Leftrightarrow\left(x^2+7x+10\right).\left(x^2+7x+12\right)-24\)

\(\Leftrightarrow\left(x^2+7x+10\right).\left(x^2+7x+10+2\right)-24\)

Đặt \(x^2+7x+10=t\), ta có

\(t.\left(t+2\right)-24\)

\(\Leftrightarrow t^2+2t-24\)

\(\Leftrightarrow t^2+2t+1-25\)

\(\Leftrightarrow\left(t-1\right)^2-25\)

\(\Leftrightarrow\left(t-1-5\right)\left(t-1+5\right)\)

\(\Leftrightarrow\left(t-6\right)\left(t+4\right)\)

\(\Rightarrow\left(x^2+7x+10-6\right)\left(x^2+7x+10+4\right)\)

\(\Leftrightarrow\left(x^2+7x+4\right)\left(x^2+7x+14\right)\)

P/s tham khảo nha

13 tháng 12 2023

\((x+5)^2+4(x+5)(x-5)+4(x^2-10x+25)=0\\\Rightarrow(x+5)^2+4(x+5)(x-5)+4(x^2-2\cdot x\cdot5+5^2)=0\\\Rightarrow(x+5)^2+2\cdot(x+5)\cdot2(x-5)+4(x-5)^2=0\\\Rightarrow(x+5)^2+2\cdot(x+5)\cdot2(x-5)+[2(x-5)]^2=0\\\Rightarrow[(x+5)+2(x-5)]^2=0\\\Rightarrow(x+5+2x-10)^2=0\\\Rightarrow(3x-5)^2=0\\\Rightarrow3x-5=0\\\Rightarrow3x=5\\\Rightarrow x=\frac53\\\text{#}Toru\)

13 tháng 12 2023

Sao đề là phân tích mà lại "= 0" vậy bạn?

27 tháng 10 2018

Đặt \(A=\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)

\(A=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)

Đặt \(x^2+7x+10=y\)

\(\Rightarrow\)\(A=y.\left(y+2\right)-24\)

\(A=y^2+2y+1-25\)

\(A=\left(y+1\right)^2-5^2\)

\(A=\left(y+1-5\right)\left(y+1+5\right)\)

\(A=\left(y-4\right)\left(y+6\right)\)

\(\Rightarrow A=\left(x^2+7x+6\right)\left(x^2+7x+16\right)\)

\(A=\left[\left(x^2+x\right)+\left(6x+6\right)\right].\left(x^2+7x+16\right)\)

\(A=\left[x.\left(x+1\right)+6.\left(x+1\right)\right].\left(x^2+7x+16\right)\)

\(A=\left(x+1\right).\left(x+6\right).\left(x^2+7x+16\right)\)

27 tháng 10 2018

Đặt \(B=\left(4x+1\right)\left(12x-1\right)\left(3x+2\right)\left(x+1\right)-4\)

\(B=\left(12x^2+11x+2\right)\left(12x^2+11x-1\right)-4\)

Đặt \(12x^2+11x-1=a\)

\(\Rightarrow B=a.\left(a+3\right)-4\)

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

\(B=\left(a^2-a\right)+\left(4a-4\right)\)

\(B=a.\left(a-1\right)+4.\left(a-1\right)\)

\(B=\left(a-1\right)\left(a+4\right)\)

\(\Rightarrow B=\left(12x^2+11x-2\right)\left(12x^2+11x+3\right)\)

11 tháng 9 2018

(x + 1)(x + 2)(x + 3)(x + 4) - 24

= x4 + 10x3 + 35x2 + 50x + 24 - 24

= x4 + 10x3 + 35x2 + 50x

11 tháng 9 2018

( x + 1 ). ( x + 2 ) ( x + 3 ) ( x + 4 ) - 24

= ( x2 + 5x + 4 ) .( x2 + 5x + 6 ) - 24

Đặt t = x2 + 5x + 5 

=> ( t - 1 ). ( t + 1 ) - 24

= t2 - 1 - 24 

= t2 - 25

= ( t - 5 ). ( t + 5 )

= ( x2 + 5x + 5 - 5 ) . ( x2 + 5x + 5 + 5 )

= ( x2 + 5x ) . ( x2 + 5x + 10 )

= x. ( x + 5 ) . ( x2 + 5x + 10 )

10 tháng 7 2021

`(x+3)^4+(x+5)^4-2`

`={[(x+3)^2]^2-1^2}+{[(x+5)^2]^2 -1^2}`

`=[(x+3)^2-1^2][(x+3)^2+1]+[(x+5)^2-1^2][(x+5)^2+1]`

`=(x+3-1)(x+3+1)[(x+3)^2+1]+(x+5-1)(x+5+1)[(x+5)^2+1]`

`=(x+2)(x+4)[(x+3)^2+1]+(x+4)(x+6)[(x+5)^2+1]`

`=(x+4){(x+2)[(x+3)^2+1]+(x+6)[(x+5)^2+1]}`

`=(x+4)(2x^3+24x^2+108x+176)`

10 tháng 7 2021

Bạn gì ơi hình như phải ra \(2\left(t+4\right)^2\left(x^2+8x+22\right)\)chứ nhỉ???