Question

aflati doua numere pozitive,stiind ca media lor aritmetica este 12,5 iar media feometrica este 10

Answer 1

Ma=(a+b)/2
(a+b)/2=12,5
a+b=12,5x2
a+b=25⇒a=25-b

Mg=√ab
√ab=10
(√ab)²=10²
ab=100

b(25-b)=100
-b²+25b-100=0                   ·(-1)
b²-25b+100=0
Δ=625-400=225
b₁=(25-15)/2=10/2=5
b₁=5
b₂=(25+15)/2=40/2=20
b₂=20
daca b₁=5 atunci a₁=25-b=25-5=20
daca b₂=20 atunci a₂=25-b=25-20=5

deci a₁=5 si b₁=20
a₂=20 si b₂=5