Răspuns:
44,(4)
Explicație pas cu pas:
(x-1)+(7x-3)+(13x-9)+(19x-27)+...+(49x-6561)=159
x+7x+13x+19x+...+49x=159+(1+3+9+27+...+6561)
x(1+7+13+19+...+49)=159+(1+3+9+27+...+6561)
in ambele paranteze avem sume a termenilor progresiilor, in prima paranteza aritmetica, iar in a doua geometrica.
Sa aflam numarul de termeni
an=a1+(n-1)·r, unde an=49, a1=1, r=6
deci 1+(n-1)·6=49, ⇒(n-1)·6=48, ⇒n-1=8, ⇒n=9 (termeni)
Atunci 1+7+13+19+...+49=9·(1+49):2=9·25=180+45=225
1+3+9+27+...+6561, unde b1=1, q=3, atunci 1+3+9+27+...+6561=1·(3^9 -1):(3-1)= (3^9 -1):2=(19683-1):2=19682:2=9841
deci x·225=159+9841, ⇒x·225=10000, ⇒x=10000:225=10000:(25·9)=400:9=44,(4)
