Question

Cum rezolv ecuatia asta: 1+3+5+....+x=81

Answer 1

stim ca 1+2+3+...+x=x(x+1)/2
 din ea scad nr pare 2+4+6+...+2x-1 ce este nr par = 2(1+2+3+...+2x+1/2)=2*(2x+1)/2*(2x+2)/2=(2x+1)(x+1) deci
x(x+1)/2- (2x+1)(x+1)=81 dau fact comun
(x+1)(x/2-2x-1)=81in a 2 paranteza aduc la ac numitor
(x+1)(x-4x-2)/2=81
(x+1)(-3x-2)=142
142=81*2=142*1=9*18
pe rand egalam 
(x+1)=81 deci x=80
(x+1)=142 deci x=141
(x+1)=9 deci x=8