Ta có

A   =   x 5   –   70 x 4   –   70 x 3   –   70 x 2   –   70 x   +   29     =   x 5   –   71 x 4   +   x 4   –   71 x 3   +   x 3   –   71 x 2   +   x 2   –   71 x   +   x   –   71   +   100     =   x 4 ( x   –   71 )   +   x 3 ( x   –   71 )   +   x 2 ( x   –   71 )   +   x ( x   –   71 )   +   ( x   –   71 )   +   100

Vì x = 71 nên x – 71 = 0, thay x – 71 = 0 vào A ta đươc

A = x 4 . 0   +   x 3 . 0   +   x 2 . 0   +   x . 0   +   0   +   100 = 100

Vậy A = 100

Đáp án cần chọn là: C

\(x=71\Leftrightarrow x-1=70\\ \Leftrightarrow A=x^5-\left(x-1\right)x^4-\left(x-1\right)x^3-\left(x-1\right)x^2-\left(x-1\right)x+34\\ A=x^5-x^5+x^4-x^4+x^3-x^3+x^2-x^2-x+x+34=34\)

\(A=x^5-70x^4-70x^3-70x^2-70x+34\)

\(=x^4\left(x-71\right)+x^3\left(x-71\right)+x^2\left(x-71\right)+x^2\left(x-71\right)+x\left(x-71\right)+x+34\)

\(=x^4\left(71-71\right)+...+x\left(71-71\right)+71+34\)

\(=x^4.0+...+x.0+105=105\)

Vì x=71

⇒70=x-1

Thay 70=x-1 ta có:

\(A=x^5-70x^4-70x^3-70x^2-70x+34\)

\(=x^5-\left(x-1\right)x^4-\left(x-1\right)x^3-\left(x-1\right)x^2-\left(x-1\right)x+34\)

\(=x^5-x^5+x^4-x^4+x^3-x^3+x^2-x^2+x+34\)

\(=x+34\)

\(=70+34\)

\(=104\)

x^5 - (x-1)x^4 -(x-1)x^3 - (x-1)x^2 - (x-1)x + 34
= x^5 - x^5 + x^4 - x^4 + x^3 - x^3 + x^2 - x^2 + x + 34 
= 71 + 34 = 105

\(A=x^5-70x^4-70x^3-70x^2-70x+34\)

\(=x^5-\left(71-1\right)x^4-\left(71-1\right)x^3-\left(71-1\right)x^2-\left(71-1\right)x+34\)

\(=x^5-\left(x-1\right)x^4-\left(x-1\right)x^3-\left(x-1\right)x^2-\left(x-1\right)x+34\)

\(=x^5-x^5+x^4-x^4+x^3-x^3+x^2-x^2+x+34\)

\(=x+34=71+34=105\)

chị mua sách giải về tham khảo nha!

chúc chị hok tốt!

\(A=x^5-70x^4-70x^3-70x^2-70x+34\)

\(\Rightarrow A=x^5-\left(x-1\right)x^4-\left(x-1\right)x^3-\left(x-1\right)x^2-\left(x-1\right)x+34\)

\(A=x^5-x^5+x^4-x^4+x^3-x^3+x^2-x^2+x+34\)

\(A=71+34\)

\(A=105\)

Với x = 71 thì x -1 = 70

\(x^5-x^4\left(x-1\right)-x^3\left(x-1\right)-x^2\left(x-1\right)-x\left(x-1\right)+34\)

\(=x^5-x^5+x^4-x^4+x^3-x^3+x^2-x^2+x+34\)

\(=71+34=105\)

Vậy biểu thức trên không phụ thuộc vào biến x

\(A=x^5-70x^4-70x^3-70x^2-70x+34\)

\(=x^5-71x^4+x^4-71x^3+x^3-71x^2+x^2-71x+x-71+105\)

\(=x^4\left(x-71\right)+x^3\left(x-71\right)+x^2\left(x-71\right)+x\left(x-71\right)+\left(x-71\right)+105\)

\(=\left(x^4+x^3+x^2+x+1\right)\left(x-71\right)+105\)

Thay x = 71\(\Rightarrow A=105\)

Vậy...

Aaaaa làm lại nha =)) tính sai .-.

Đặt 70 = x - 1 ; 34 = x - 37. Ta có :

$A=x^5-(x-1)x^4-(x-1)x^3-(x-1)x^2-(x-1)x+x-37$

$=>A=x^5-x^5+x^4-x^4+x^3-x^3+x^2-x^2+x+x-37$

$=>A=2x-37=2.71-37=105$

Đặt 70 = x - 1 ; 34 = x - 37. Ta có :

$A=x^5-(x-1)x^4-(x-1)x^3-(x-1)x^2-(x-1)x+34$

$=>A=x^5-x^5+x^4-x^4+x^3-x^3+x^2-x^2+x-x-37$

$=>A=-37$

Ta có: \(x=71\Rightarrow\left\{{}\begin{matrix}x-1=70\\x-37=34\end{matrix}\right.\)

Thay \(x-1=70\) và \(x-37=34\) vào biểu thức, ta được:

\(A=x^5-\left(x-1\right)x^4-\left(x-1\right)x^3-\left(x-1\right)x^2-\left(x-1\right)x+x-37\)

\(\Leftrightarrow A=x^5-x^5+x^4-x^4+x^3-x^3+x^2-x^2+x+x-37\)

\(\Leftrightarrow A=2x-37\)

Thay \(x=71\) vào ta được:

\(A=2\cdot71-37=142-37=105\)