Question

Tính A= x¹⁰⁰-21x⁹⁹-21x⁹⁸-21x⁹⁷-...-21x²-21x+2010 với x=22

Answer 1

^{A = x^100 - 21x^99 - 21x^98 - 21x^97 -...-21x^2 - 21x +2010}

^{A=x^100 - 22x^99 + x^99 -22x^98 + x^98 - ... - 22x +x +2010}

^{A=x^99 (x-22) + x^98 (x-22) + x^97(x-22) + ... + x(x-22) + x +2010}

^{A=(x-22) (x^99 + x^98 + x^97 + ... + x) + x + 2010}

Thay x = 22 vào A, tao có:

A= (22-22) (22^99 + 22^98 + ... +22) + 22 + 2010

A = 0 (22^99 + 22^98 + ... +22) + 2032

A= 0 + 2032

A = 2032

Answer 2

x=22

=>x-1=21

thay 21=x-1 vào A ta được:

A=x¹⁰⁰-(x-1)x⁹⁹-(x-1)x⁹⁸-(x-1)x⁹⁷-...-(x-1)x²-(x-1)x+2010

=x¹⁰⁰-x¹⁰⁰+x⁹⁹-x⁹⁹+x⁹⁸-x⁹⁸+x⁹⁷-...-x³+x²-x²+x+2012

=>A=x+2012

thay x=22 vào A=x+2012 ta được:

A=22+2012=2034