\(R=x^4\left(x-2345\right)+2345x^2\left(x-1\right)+2345\left(x-1\right)\)\(=-x^4+x^2\left(x+1\right)\left(x-1\right)+\left(x-1\right)\left(x+1\right)\)\(=-x^4+x^4-x^2+x^2-1=-1\)
Coi lại giúp mình nha

\(gt\Rightarrow x+1=2345\)

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

\(R=x^5-x^5-x^4+x^4+x^3-x^3-x^2+x^2+x-x-1\)

\(R=-1\)

x^5-(x+1)x^4+(x+1)x^3-(x+1)x^2+(x+1)x-(x+1)

tự làm tiếp đi

1234567890-12345

Lời giải:

Ta biến đổi $R$ như sau :

\(R=x^5-2344x^4-x^4+2344x^3+x^3-2344x^2-x^2+2344x+x-2344-1\)

\(=(x^5-2344x^4)-(x^4-2344x^3)+(x^3-2344x^2)-(x^2-2344x)+(x-2344)-1\)

\(=x^4(x-2344)-x^3(x-2344)+x^2(x-2344)-x(x-2344)+(x-2344)-1\)

\(=(x-2344)(x^4-x^3+x^2-x+1)-1\)

Tại $x=2344$ thì \(x-2344=0\). Do đó:

\(R=0.(x^4-x^3+x^2-x+1)-1=-1\)

x + ( x + 1 ) + ( x + 2 ) + .... + ( x + 2344 ) + 2345 = 2345

      ( có 2346 số hạng ) 

x + ( x + 1 ) + ( x + 2 ) + ..... + ( x + 2344 ) = 2345 - 2345

x + ( x + 1 ) + ( x + 2 ) + ..... + ( x + 2344 ) = 0

 ( có 2345 số hạng )

[ ( x + 2344 ) + x ] . 2345 : 2 = 0

[ ( x + 2344 ) + x ] . 2345 = 0 . 2

( 2x + 2344 ) . 2345 = 0

2x + 2344 = 0 : 2345

2x + 2344 = 0

2x = 0 - 2344

2x = - 2344

x = - 2344 : 2 = - 1172

Vậy x = - 1172 

Câu 2:

\(a\cdot\left(b-c\right)-b\left(a+c\right)\)

\(=ab-ac-ab-bc\)

\(=-ac-bc=-c\left(a+b\right)\)