x=7

nên x+1=8

\(A=x^{15}-x^{14}\left(x+1\right)+x^{13}\left(x+1\right)-...-x^2\left(x+1\right)+x\left(x+1\right)-5\)

\(=x-5=7-5=2\)

chat vs t

 Ta có x =7  

=>x+1=8

\(\Rightarrow\)\(A=x^{15}-8x^{14}+8x^{13}-8x^{12}+.......8x^2+8x-5\)

\(\Rightarrow x^{15}-\left(x+1\right)x^{14}+\left(x+1\right)x^{13}-\left(x+1\right)x^{12}+...\left(x+1\right)x^2\)

\(+\left(x+1\right)x^5\)

\(\Rightarrow x^{15}-x^{15}-x^{14}+x^{14}+x^{13}-x^{13}-x^{12}+...-x^3-x^2+x-5\)

\(\Rightarrow x-5\Leftrightarrow A=7-5=2\Rightarrow A=2\)

Vậy A=2 khi x=7

Vì x=7 nên 8 = x + 1

  Thay 8 = x + 1 vào biểu thức A ta có 

 \(A=x^{15}-x^{14}\left(x+1\right)+x^{13}\left(x+1\right)-x^{12}\left(x+1\right)+....-x^2\left(x+1\right)+x\left(x+1\right)-5\)

     \(=x^{15}-x^{15}-x^{14}+x^{14}+x^{13}-x^{13}-x^{12}+....-x^3-x^2+x^2+x-5\)

      \(=x-5\)

  Mà x = 7

 Nên \(A=7-5\)

             \(=2\)

  Vậy A = 2 tại x=7

x=7

=>x+1=8

=> A= x^15 - 8x^14 + 8x^13 - 8x^12 +....- 8x^2 + 8x - 5 

=x¹⁵-(x+1)x¹⁴+(x+1)x¹³-(x+1)x¹²+...-(x+1)x²+(x+1)x-5

=x¹⁵-x¹⁵-x¹⁴+x¹⁴+x¹³-x¹³-x¹²+...-x³-x²+x²+x-5

=x-5

=>A=7-5=2

Vậy A=2 khi x=7

\(B=x^{15}-8x^{14}+8x^{13}-8x^{12}+...+8x-5\)

\(=x^{15}-\left(x+1\right)x^{14}+\left(x+1\right)x^{13}-\left(x+1\right)x^{12}+...+\left(x+1\right)x-x+2\)

\(=x^{15}-x^{15}-x^{14}+x^{14}+x^{13}-x^{13}-x^{12}+...+x^2+x-x+2\)

\(=2\)

Ta có:

x = 7

=> x + 1 = 8 (1)

Thay (1) vào biểu thức ta được

\(x^{15}-\left(x+1\right)x^{14}+\left(x+1\right)x^{13}-\left(x+1\right)x^{12}+...-\left(x+1\right)x^2+\left(x+1\right)x-5\)

\(=x^{15}-x^{15}-x^{14}+x^{14}+x^{13}-x^{13}-x^{12}+...-x^3-x^2+x^2+x-5\)

\(=x-5\)

\(=7-5\)

\(=2\)

Ta có :

= x^15 - 8x^14 + 8x^13 - 8x^12 +... - 8x² + 8x - 5
= x^15 - 8x^13(x - 1) - 8x^11(x-1) +... - 8x(x - 1) - 5
= x^15 - 8(x - 1)(x^13 + x^11 +... + x) - 5 (♠)
Xét : A = x^13 + x^11 + x^9 + x^7+... + x³ + x
⇔ x².A = x^15 + x^13 + x^11 + x^9 + x^7 +... + x³
⇔x².A - A = (x^15 + x^13 + x^11 + x^9 +... + x³) - (x^13 + x^11 + x^9 + x^7+... + x) = x^15 - x
⇔ A = (x^15 - x)/(x² - 1)
Thay vào (♠) ta được :
P = x^15 - 8(x - 1)(x^15 - x)/(x² - 1) - 5
= x^15 - 8(x^15 - x)/(x + 1) - 5
Thay x = 7 vào biểu thức trên ta được : P = 7^15 - 8(7^15 - 7)/(7+1) - 5 = 2
Vậy giá trị của biểu thức bằng 2

thay x=7

ta có:7^15-8*7^14+887^13-8*7^12+...-8*7^2+8*7-2015

f(7)=7^15-8.7^14+8.7^13-8.7^12+... 
-8.7^2+8.7-5= 
= -7^14+8.7^13-8.7^12+...-8.7^2+8.7-5= 
=7^13-8.7^12+...-8.7^2+8.7-5= 
= -7^12+...-8.7^2+8.7-5= 
=...= -7^2+8.7-5=7-5=2 
Kết quả là 2

sao mà 2 câu giống nhau thế

f(7)=7^15-8.7^14+8.7^13-8.7^12+... 
-8.7^2+8.7-5= 
= -7^14+8.7^13-8.7^12+...-8.7^2+8.7-5= 
=7^13-8.7^12+...-8.7^2+8.7-5= 
= -7^12+...-8.7^2+8.7-5= 
=...= -7^2+8.7-5=7-5=2 
Kết quả là 2

\(x^{15}-\left(7+1\right)x^{14}+\left(7+1\right)x^{13}....+\left(7+1\right)x-5\)

\(=x^{15}-\left(x+1\right)x^{14}+\left(x+1\right)x^{13}....+\left(x+1\right)x-5\)

\(=x^{15}-x^{15}-x^{14}+x^{14}+x^{13}....-x^3-x^2+x^2+x-5\)

\(=x-5=7-5=2\)

ai ma biet

x=7 nen x+1=8

\(A=x^{15}-x^{14}\left(x+1\right)+x^{13}\left(x+1\right)-...+x^3\left(x+1\right)-x^2\left(x+1\right)+x\left(x+1\right)-5\)

\(=x^{15}-x^{15}-x^{14}+x^{14}+...+x^4+x^3-x^3-x^2+x^2+x-5\)

=x-5

=2