Question

2. cho f(x)= x⁸-101x⁷+101x⁶-101x⁵+...+ 101x²-101x+25. tính f(100)?

Answer 1

Vì x=100 nên x+1=101

Thay 101=x+1 vào f(x) ta có:

f(x) = x⁸ - (x+1)x⁷ + (x+1)x⁶ -(x+1)x⁵ + ... + (x+1)x² -(x+1)x +25

= x⁸ -x⁸ - x⁷ + x⁷ +x⁶-x⁶-x⁵ + ... + x³ + x² - x² -x+25

= x+25

=> f(100) = 100+25=125

Vậy f(100) = 125

Answer 2

Cách2:

f(100) = 100⁸ - 101.100⁷ + 101.100⁶-101.100⁵+...+101.100²-101.100+25

=100⁸-(100+1)100⁷+(100+1)100⁶-(100+1)100⁵+...+(100+1)100²-(100+1)100+25

=100⁸-100⁸-100⁷+100⁷+100⁶-100⁶+100⁵+...+100³+100 -100²-100+25

=-100+25=75

Vậy f(100)=75

Answer 3

cách 1: mk sửa chỗ =x+25 thành =-x+25

=> f(100)=-100+25=75

Vậy f(100)=75

Answer 4

vì x=100=)x+1=101

f(X)=x⁸-(x