Let the three positive consecutive natural numbers be x, x + 1 and x + 2, respectively. According to the question, [x+x+1+x+2]2−[x2+(x+1)2+(x+2)2] = 292 ⇒[3x+3]2−[x2+x2+1+2x+x2+4+4x]=292 ⇒9x2+9+18x−3x2−6x−5=292 ⇒6x2+12x+4−292=0 ⇒x2+2x−48=0 ⇒x2+8x−6x−48=0 ⇒x(x+8)−6(x+8)=0 ⇒(x+8)(x−6)=0 ∴x=6 The largest of the three numbers =x+2=6+2=8