Question

Determina numarul natural n care verifica egalitatea:1^n•[(3^5)^2-3^12:3^9•3^7]=2^0

Answer 1

n(n+1)(n+2)=990

(n la puterea 2+n)(n+2)=990

n la puterea 3 +2n la puterea 2 +n la puterea 2 +2n=990

n la puterea 3 +3n la puterea 2 +2n=990

n la puterea 3 +3n la puterea 2 +2n-990=0

n la puterea 3 -9 n la puterea 2 +12 n la puterea 2 -108n+110n-990=0

n la puterea 2 ×(n-9)+12n×(n-9)+110×(n-9)=0

(n-9)×(n la puterea 2 +12n+110)=0

n-9=0

n la puterea 2 +12n+110=0

n=9

(n nu apartine lui R)