Question

determinati numarul natural x, stiind ca (x+1) × (x+2) + (x+2) × (x+3) = 50

Answer 1

(x+1) × (x+2) + (x+2) × (x+3) = 50
(x+2)(x+1+x+3) = 50
(x+2)(2x+4) = 50
(x+2)(x+2) = 25
x+2=5
x=3

Answer 2

(x+1)(x+2)+(x+2)(x+3)=50
x²+2x+x+2+x²+3x+2x+6=50
2x²+8x+8=50
2x²+8x-42=0

delta=b²-4ac=8²-4*2*(-42)=64+8*42=64+336=400
x1(1 este indice)=(-b+√delta)/2a=(-8+√400)/2*2=(-8+20)/4=12/4=3
x2(2 este indice)=(-b-√delta)/2a=(-8-√400)/2*2=(-8-20)/4=-28/4=-7

x⊂N
x={3}