Question

Se stie ca x-y+2z=5. Calculati suma:
S=(x-y+2z)+(2x-2y+4z)+...+(10x-10y+20z)

Answer 1

Faci asa: dupa cum observi daca inmultesti pe x-y+2z cu 2 iti da 2x-2y+4z=2*5=10. Asa faci la fiecare .Deci :x-y+2z+(x-y+2z)*2 +(x-y+2z)*10= 5+2*5+10*5=5+10+50=65

Answer 2

Observam ca in fiecare termen avem ca factor comun pe x-y+2z.
=> S = (x-y+2z)(1+2+...+10) => S = 5 * (10 * 11) : 2 => S = 5 * 5 * 11 =>
=> S = 5 * 55 = 275