Question

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

Answer 1

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

f(x)=x⁸-101x⁷+101x⁶-101x⁵+...+101x²-101x+25

=x⁸-(100+1)x⁷+(100+1)x⁶-(100+1)x⁵+...+(100+1)x²-(100+1)x+25

f(100 ) hay x= 100

Thay 100 = x ,có :

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

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

= x+ 25

f(100 0 = 100 + 25 = 125

Vậy f(100 ) =125