Question

bài 1 :rút gọn A= (2+1).(2²+1).(2⁴+1).....(2²⁵⁶+1) + 1

bài 2 : a,cho x/a+y/b+z/c=0₍₁₎ và a/x+b/y+c/z=2 . tính A=x²/a²+y²/b²+z²/c²

b,rút gọn B=(ab/(a²+b²+c²))+(bc/(b²+c²+a²))+(ca/(c²+a²+b²))

bài 3: tìm x 

((x-1)/2006)+((x-10)/1997)+((x-19)/1988)=3

Answer 1

Bài 1: 

Ta có: \(A=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{256}+1\right)+1\) 

\(=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{256}+1\right)+1\)

\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{256}+1\right)+1\)

\(=\left(2^4-1\right)\left(2^4+1\right)...\left(2^{256}+1\right)+1\)

\(............................\)

\(A=\left[\left(2^{256}\right)^2-1\right]+1=2^{512}\)