\(a) f ( x ) = 2 x ^4 + 3 x ^2 − x + 1 − x ^2 − x ^4 − 6 x ^3\)

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

\(= x ^4 − 6 x ^3 + 2 x ^2 − x + 1\)

\(g ( x ) = 10 x ^3 + 3 − x ^4 − 4 x ^3 + 4 x − 2 x ^2\)

\(= − x ^4 + ( 10 x ^3 − 4 x ^3 ) − 2 x ^2 + 4 x + 3\)

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

\(b) f ( x ) + g ( x ) = x ^4 − 6 x ^3 + 2 x ^2 − x + 1 − x ^4 + 6 x ^3 − 2 x ^2 + 4 x + 3\)

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

\(= 3 x + 4\)

c)Có \(h ( x ) = f ( x ) + g ( x ) = 3 x + 4\)

\(Cho h ( x ) = 0 ⇒ 3 x + 4 = 0\)

\(⇒ 3 x = − 4\) 

\(⇒ x = − \frac{4 }{3} \)

Vậy  \(x=-\frac{4}{3}\) là nghiệm của \(h ( x ) \)

Ở bên trên, mình viết nhầm, đề bài là:

Cho P(x)=x^99-100x98+100x97-100x^96+...+100x-1. Tính P(99)

Mong mọi người giúp đỡ

Ta có : x = 99

=> 100 = x + 1 

Thay vào A ta có : A = x²⁰¹⁸ - 100x²⁰¹⁷ + 100x²⁰¹⁶ - ...... + 100x² - 100x + 2019

=> A = x²⁰¹⁸ - (x + 1)x²⁰¹⁷ + (x + 1)x²⁰¹⁶ - ...... + (x + 1)x² - (x + 1)x + 2019

=> A = x²⁰¹⁸ - x²⁰¹⁸ - x²⁰¹⁷ + x²⁰¹⁷ + x²⁰¹⁶ -.......+ x³ + x² - x² + x + 2019

=> A = x + 2019

=> A = 99 + 2019

=> A = 2118

P/s : ko cần ! :D 

Theo đề bài ra ta có :

x = 99  

Thay vào A ta có :

A = x²⁰¹⁸ - 100x²⁰¹⁷ + 100x²⁰¹⁶ - ... + 100x² - 100x + 2019

\(\Rightarrow\) A = x²⁰¹⁸ - ( x + 1 ) x²⁰¹⁷ + ( x + 1 ) x²⁰¹⁶ - ... + ( x + 1 ) x² - ( x + 1 ) x + 2019

\(\Rightarrow\) A = x²⁰¹⁸ - x²⁰¹⁸ - x²⁰¹⁷ + x²⁰¹⁷ + x²⁰¹⁶- ... + x³ + x² - x² + x + 2019

\(\Rightarrow\) A = x + 2019

\(\Rightarrow\) A = 99 + 2019

\(\Rightarrow\) A = 2118 

bn chưa ngủ ak 

h giái giúp mk đy

A=\(x^5-100x^4+100x^3-100x^2+100x-9\)

  =\(x^5-\left(99+1\right)x^4+\left(99+1\right)x^3-\left(99+1\right)x^2+\left(99+1\right)x-9\)

Thay 99=x vào ta được:

A=\(x^5-\left(x+1\right)x^4+\left(x+1\right)x^3-\left(x+1\right)x^2+\left(x+1\right)x-9\)

  =\(x^5-x^5-x^4+x^4+x^3-x^3-x^2+x^2+x-9\)

  =x-9

thay x=99 vào ta được:

A=99-9=90

Vậy giá trị của biểu thức A tại x=99 là 90

\(p\left(x\right)=x^{99}-100x^{98}+100x^{97}-....+100x-1\)

Ta có: \(x=99\Rightarrow x+1=100\)

\(\Rightarrow p\left(99\right)=x^{99}-\left(x+1\right)x^{98}+\left(x+1\right)x^{97}-...+\left(x+1\right)x-1\)

\(=x^{99}-x^{99}-x^{98}+x^{98}+x^{97}-...+x^2+x-1\)

\(=x-1\)

\(=99-1\)

\(=98\)

p(x)=x^99-100x^98+100x^97-...+100x-1

vì x=99=>x+1=100=>p(99)=x^99-(x+1)x^98+(x+1)x^97-...+(x+1)x-1

=x^99-x^99-x^98+x^98+x^97-...+x^2+x-1

=x-1

=99-1

=98

x =99 => 100 = x + 1 thay vào ta có 

\(x^5-\left(x+1\right)x^4+\left(x+1\right).x^3-\left(x+1\right).x^2+\left(x+1\right)x-9=x^5-x^5-x^4+...+x^2+x-9\)

= x - 9

= 99 -9 

= 90

P=x3+y3+2xy=(x+y)3−3xy(x+y)+2xy=2013−601xy" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">P=x3+y3+2xy=(x+y)3−3xy(x+y)+2xy=2013−601xy

S=xy=x(201−x)" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">S=xy=x(201−x)

1≤x≤200" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">1≤x≤200

S=200−(x−1)(x−200)≥0⇒Smin=200" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">S=200−(x−1)(x−200)≥0⇒Smin=200

x≤y⇒x≤100" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">x≤y⇒x≤100

S=100.101−(x−100)(x−101)≤100.101⇒Smax=100.101" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">S=100.101−(x−100)(x−101)≤100.101⇒Smax=100.101

Ta có 100=99+1 hay x+1

Thay x+1 vào P(99) .Ta có :\(x^{99}-\left(x+1\right)x^{98}+\left(x+1\right)x^{97}-..................+\left(x+1\right)x-1\)=\(x^{99}-x^{99}-x^{98}+x^{98}+x^{97}-.............+x^2+x-1\) =\(\left(x^{99}-x^{99}\right)-\left(x^{98}-x^{98}\right)+\left(x^{97}-x^{97}\right)-.........+\left(x^2-x^2\right)+x-1^{ }\)

=x-1=99-1=98

\(P\left(x\right)=x^{99}-100x^{98}+100x^{97}-...+100x-1\)

\(P\left(99\right)=99^{99}-100\cdot99^{98}+100\cdot99^{97}-...+100\cdot99-1\)

\(P\left(99\right)=99^{99}-\left(99+1\right)\cdot99^{98}+\left(99+1\right)\cdot99^{97}-...+\left(99+1\right)\cdot99-1\)

\(P(99)= 99^{99}-99^{99}-99^{98}+99^{98}+99^{97}-99^{97}-99^{96}+...+99^2+99-1\)

\(P\left(99\right)=99-1=98\)