Question

Aflați suma a 4 nr naturale consecutive a b c d dacă a×b×c=720

Answer 1

a,b,c,d consecutive deci

b=a+1

c=b+1=a+1+1=a+2

d=c+1=a+2+1=a+3

a×b×c=720

a(a+1)(a+2)=720

(a²+a)(a+2)=720

a³+2a²+a²+2a=720

a³+3a²+2a=720

a³+3a+2a-720=0

(a-8)(a²+11a+90)=0

a-8=0

a=8

a²+11a+90=0

∆=121-4×90×1=-239 ceea ce nu are soluții reale, deci ultima solutie este 8

a=8

b=9

c=10

d=11

a+b+c+d=8+9+10+11=38