Question

Rezolvati sistemele
x+2x+3x+...+50x-2y=0
x-2x+3x-4x+...+49x-50x+8y=0
Multumesc!

Answer 1

1.Mai intai faci suma lui gauss (x+....+50x) si scazi 2y.
2.la fel pana la 49x si scazi 50x apoi aduni 8y=0
3.-2y=suma data de gauss(n(n+1)/2) .... y=s gauss/-2
4.inlocuiesti in ecuatia 2 ,in   8y=s gauss-50x
5 continua ecuatia

Answer 2

x(1+2+3+........+50) -2y = 0      50·51/2 ·x - 2y = 0      1275x -2y = 0      (1)
x(1-2+3-4+......+49-50) +8y =0  (-1)·x·25 +8y = 0          -25x + 8y = 0      (2)
din 4·(1) +( 2) ⇒ 5075x = 0    x = 0    y = 0