Question

x•7+x•14+x•21+x•28+....+x•126=7•9•19

Answer 1

X•7+x•14+x•21+x•28+....+x•126=7•9•19
x(7+14+28+...+126)=7·9·19
x·7·(1+2+3+...+18)=7·9·19 |:7
x(1+2+3+...+18)=9·19

$x*\frac{18*19}{2}=9*19$

$x*9*19=9*19 |:(9*19)$

=> $\boxed{x=1}$

SUMA LUI GAUS: $1+2+3+...+n=\frac{n(n+1)}{2}$

Answer 2

x•7+x•14+x•21+x•28+....+x•126=7•9•19

7x ×( 1 + 2 + 3 + 4 +...+ 18) = 7 × 9 × 19

7x × 18 × (18+1) : 2 = 7 × 9 × 19

7x × 9 × 19 = 7 × 9 × 19

x = (7 × 9 × 19) : (7 × 9 × 19)

x = 1