Aflati valoarea lui x din:x+2x+3x+.....+30x=166a,166a:2

x+2x+3x+.....+30x=166a
x(1+2+...+30)=166a
x*(1+30)*30/2=166a
x*31*15=166a
x*465=166a
Deoarece 166a divizibil cu 2 => 166a∈{1660,1662,1664,1666,1668}
1)x*465=1660⇒x=332/93
2)x*465=1662⇒x=554/155
3)x*465=1664⇒x=1664/465
4)x*465=1666⇒x=1666/465
5)x*465=1668⇒x=556/155

Answer Link

Аноним Аноним · Answer 2 · 2015-12-30T00:36:46+02:00

____ ____
x+ 2x+ 3x+ ...+ 30x= 1 66a   1 66a : 2 , a ∈ {0; 2; 4; 6; 8}

1. pt. a= 0 ⇒ x+ 2x+ 3x+ ...+ 30x= 1 660
    x(1+ 2+ 3+ ...+ 30)= 1 660
x·30·31:2= 1 660
   x·15·31= 1 660
    x·465= 1 660
x=1 660: 465
x= 3, 5

2. pt a= 2⇒ x+ 2x+ 3x+ ...+ 30x= 1 662
    x(1+ 2+ 3+ ...+ 30)= 1 662
   x·30·31:2= 1 662
   x·15·31= 1 662
    x·465= 1 662
x=1 662: 465
    x= 3, 5

3. pt. a= 4⇒ x+ 2x+ 3x+ ...+ 30x= 1 664
    x(1+ 2+ 3+ ...+ 30)= 1 664
   x·30·31:2= 1 664
   x·15·31= 1 664
    x·465= 1 664
x=1 664: 465
    x= 3, 5

4. pt.a= 6 ⇒ x+ 2x+ 3x+ ...+ 30x= 1 666
    x(1+ 2+ 3+ ...+ 30)= 1 666
   x·30·31:2= 1 666
   x·15·31= 1 666
    x·465= 1 666
x=1 666: 465
    x= 3, 5

5. pt.a= 8 ⇒ x+ 2x+ 3x+ ...+ 30x= 1 668
    x(1+ 2+ 3+ ...+ 30)= 1 668
   x·30·31:2= 1 668
   x·15·31= 1 668
    x·465= 1 668
x=1 668: 465
    x= 3, 5