Question

Aflați x din: 1+2+3+...+2004/ 2+4+6+...+2004= 2x-1/ x

Answer 1

Răspuns:  x = 1003

Explicație pas cu pas:

(1+2+3+....+2004)/(2+4+6+....+2004) = (2x-1)/x

Calculez sumele:

2004×(1+2004):2 = 1002 ×2005 ->  numaratorul

2×(1+2+3+...+1002)= 2×1002 ×(1+1002):2 = 1002 × 1003 -> numitorul

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(1002× 2005)/(1002×1003) = (2x-1)/x

->  simplific prima fractie prin 1002

2005/1003 = (2 x -1)/x

2005 x = 1003×(2x - 1) → produsul mezilor = produsul extremilor

2005 x = 2006 x - 1003

2006 x - 1003 = 2005 x

2006 x - 2005 x = 1003

x = 1003

Answer 2

$\frac{1+2+..+2004}{2+4+..+2004}=\frac{2x-1}{x}\\\\\frac{2004*2005:2}{2(1002*1003:2)}=\frac{2x-1}{x}\\\\\frac{1002*2005}{1002*1003}=\frac{2x-1}{x}$

2005x=1003(2x-1)

2005x=2006x-1003

1003=2006x-2005x

x=1003