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x4-2014x3+2014x2-2014x+2014 = x4 - 2013x3 - x3 + 2013x2 + x2 +2013x + x + 2014
= x4 - 2013 (x3-x2+1) - (x3-x2+1) + 2014
= x4 -2014 (x3-x2+1) + 2014 = x4 - 2014 (x3-x2) = x4 - 2014 x2 (x-1) = x2 ( 20132 - 2014.2012) = x2 [20132 - (2013+1).(2013-1)]
= x2 = 20132
giúp tôi giải bài toán này giùm nhal bạn :/x+1/+/x+2/+/x+3/+...+/x+2013/=2014x
trả lời
xx^4+2015x^2+2014x+2015=x^4+2015x^2+2015x-x+2015=x\left(x^3-1\right)+2015\left(X^2+x+1\right)=x\left(x-1\right)\left(x^2+x+1\right)+2015\left(x^2+x+1\right)=\left(x^2+x+1\right)\left(x^2-x+2015\right)xx4+2015x2+2014x+2015=x4+2015x2+2015x−x+2015=x(x3−1)+2015(X2+x+1)=x(x−1)(x2+x+1)+2015(x2+x+1)=(x2+x+1)(x2−x+2015)
hc tốt
\(x^4+2015x^2+2014x+2015\)
\(=\left(x^4-x\right)+2015x^2+2015x+2015\)
\(=x\left(x^3-1\right)+2015\left(x^2+x+1\right)\)
\(=x\left(x-1\right)\left(x^2+x+1\right)+2015\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^2-x+2015\right)\)
x4+2015x2+2014x+2015
=x4-x+2015x2+2015x+2015
=x.(x3-1)+2015.(x2+x+1)
=x.(x-1)(x2+x+1)+2015.(x2+x+1)
=(x2+x+1)(x2-x+2015)
\(x^4+2015x^2+2014x+2015=\left(x^4+x^3+x^2\right)-\left(x^3+x^2+x\right)+\left(2015x^2+2015x+2015\right)\)
\(=x^2\left(x^2+x+1\right)-x\left(x^2+x+1\right)+2015\left(x^2+x+1\right)=\left(x^2+x+1\right)\left(x^2-x+2015\right)\)
\(x^4+2015x^2+2014x+2015\)
\(=\left(x^4-x^3+2015x^2\right)+\left(x^3-x^2+2015x\right)+\left(x^2-x+2015\right)\)
\(=\left(x^2-x+2015\right)\left(x^2+x+1\right)\)
x^4-2014x^2+2015x-2014=0
<=>x4+x-2014x2+2014x-2014=0
<=>x.(x3+1)-2014.(x2-x+1)=0
<=>x.(x+1)(x2-x+1)-2014.(x2-x+1)=0
<=>(x2+x+1)[x.(x+1)-2014]=0
<=>x.(x+1)-2014=0 (vì x2+x+1 >0)
giải tiếp sao số xấu thế
ta có:
x^4+2014x^2+2013x+2014 = x^4+2013x^2+x^2+2013x+2013+1
=(x^4+x^2+1)+2013(x^2+x+1)
=(x^2+1)^2-x^2+2013(x^2+x+1)
=(x^2-x+1)(x^2+x+1)+2013(x^2+x+1)
=(x^2+x+1)(x^2+x+2014)
x4+2014x2+2013x+2014=(x4-x)+(2014x2+2014x+2014)
=x(x-1)(x2+x+1)+2014(x2+x+1)
=(x^2+x+1)(x2-x+2014)
A= x2015 - 2014x2014 - 2014x2013 - ...- 2014x2 - 2014x + 1
= x2015 - (2015-1)x2014 - (2015-1)x2013 -...- (2015-1)x2 - (2015-1)x + 1
= x2015 - 2015x2014+1 - 2015x2013+1 -...- 2015x2+1 - 2015x+1+1
= x2015 - 2015x2014 - 2015x2013 -...- 2015x2 - 2015x+ (1+1+1+...+1)
Thay x= 2015 vào biểu thức ta có:
=20152015 - 20152015 - 20152014-...- 20153 - 20152+2015
=0 - 2.20152014 -...- 2.20153 - 20152 + 2015
= -2.( 20152014 - ...- 20153) - 20152+2015