Question

Aflati trei numere zecimale , stiind ca doua cate doua au mediile aritmetice 4,(7) ; 8,(6) ; si 3,(2)

Answer 1

a,b,c numere
media aritmetica:

(a+b)/2=4.(7)    4.(7)=4 (7/9)=(9*4+7)/9=43/9
(b+c)/2=8.(6)    8.(6)=8(6/9)=78/9
(a+c)/2=3.(2)    3.(2)=3(2/9)=29/9

(a+b)/2=43/9 

9(a+b)=43*2
9a+9b=86
9a=86-9b
 introducem intr-a 3-a ecuatie

(a+c)/2=29/9
9a+9c=29*2
86-9b+9c=58
28=9b-9c
9b-9c=28
9b= 28+9c introducem intr-a 2-a

(b+c)/2=78/9
9b+9c=78*2
28+9c+9c=156
28+18c=156
18c=128
c=128/18=64/9=7.(1)    c=7.(1)

9b=28+9c
9b=28+64/9
81b=28*9+64
81b= 252+64
81b=316
b=316/81=3.901        b=3.901


9a=86-9b
9a=86-9*316/81
9a=86-316/9
81a= 9*86-316
81a=774-316
a=458/81=5.65      a=5.65