Question

sa se calculeze suma nr naturale ab stiind ca ab+ba=110

Answer 1

$\overline{ab}+\overline{ba} = 110\\ (10a+b)+(10b+a) = 110\\ 11a+11b = 110 \\ 11(a+b) = 110\\ a+b = 110:11 \\ a+b = 10$

Answer 2

Răspuns:

495

Explicație pas cu pas:

ab+ba=110

10a+b+10b+a=110, ⇒11a+11b=110, ⇒11·(a+b)=110, ⇒a+b=110:11, ⇒a+b=10

a,b∈{1,2,3,4,5,6,7,8,9}

⇒(a;b)∈{(1;9),(2;8),(3;7),(4;6),(5;5),(6;4),(7;3),(8;2),(9;1)}, pentru care a+b=10

Atunci ab∈{19,28,37,46,55,64,73,82,91}

Suma=19+28+37+46+55+64+73+82+91=(19+91)+(28+82)+(37+73)+(46+64) + 55 = 110+110+110+110+55=4·110+55=440+55=495