Question

aflati numerele a si b stiind ca suma lor este 49 iar cel mai mare divizor comun 7
Va rog repede

Answer 1

a + b = 49

a = 7x

b = 7y

7x + 7y = 49

7 (x + y) = 49

(x + y) = 49 : 7

x + y = 7

(x,y) ∈ {(1,6) ; (2,5); (3,4)}

(a,b) ∈ {(7,42); (14,35) ; (21,28)}

Answer 2

a+b=49

cmmdc al lui a si b=7 =>

a=7×x
b=7×y

7×x+7×y=49
7×(x+y)=49
x+y=49:7
x+y=7

cautam toate probabilitățile lui x si y pana aflăm cu cat sunt egale =>

daca x=1 => y=7-1=6

x+y=1+6=7

a=7×x=7×1=7
b=7×6=42

7+42=49 (adevarat )

___________________

daca x=2 => y=7-2=5

x+y=2+5=7

a=7×x=7×2=14
b=7×y=7×5=35

a+b=14+35=49 (adevărat)

_____________________

daca x=3 => y=7-3=4

x+y=3+4=7

a=7×x=7×3=21
b=7×y=7×4=28

a+b=21+28=49 (adevărat )



__________________


daca x=4 => y=7-4=3

x+y=4+3=7

a=7×x=7×4=28
b=7×y=7×3=21

a+b=28+21=49 (adevărat )


_____________________

daca x=5 => y=7-5=2

x+y=5+2=7

a=7×x=7×5=35
b=7×y=7×2=14

a+b=35+14=49 (adevărat )

__________________

daca x=6 => y=7-6=1

x+y=7

a=7×x=7×6=42
b=7×y=7×1=7

a+b=42+7=49 (adevarat )

a={7, 14, 21,28, 35,42}

b={ 42,35,28,21,14,7 }