Question

x+3x+5x+7x+.......+59x=5400

Answer 1

Răspuns: x = 6

Explicație pas cu pas:

x + 3 x + 5 x + 7 x + ..... + 59 x = 5 400

x ( 1 + 3 + 5 + 7 + ..... + 59 ) = 5 400

1 + 3 + 5 + 7 + .... + 59 =  30 × ( 1 + 59 ) : 2

→ ( 59 - 1 ) : 2 + 1 = 58 : 2 + 1 = 30 termeni are suma

→ aplic formula sumei lui Gauss:

x ( 30 × 60 : 2 ) = 5 400

x ( 30 × 30 ) = 5 400

x · 900 = 5 400

x = 5 400 : 900

x = 6

Answer 2

Dam factor comun pe x:

x(1+3+5+...+59)=5400

1=1

3=1+2

5=2+3

.................

57=28+29

59=29+30

_________+

1+3+5+7+...+59=1·2 +2·2 +3·2+...+29·2 +30=

=2(1+2+3+...+29)+30=

=2·((29·30):2)+30=

=29·30+30=

=30(29+1)=

=30·30=

=900

=> x·900=5400

x=5400:900

x=6