Question

Determinati numerele reale pozitive a , b si c stiind ca media geometrica a nr. a si b e 3radical din 2, media geometrica a nr. b si c e 6 si media geometrica a nr. a si c e 2 radical din 6.

Answer 1

Mg=√ab
√ab=3√2
(ab)²=(3√2)²
ab=18
√bc=6
(√bc)=6²
bc=36
√ac=2√6
(√ac)²=(2√6)²
ac=24
din ab=18⇒a=18/b
din bc=36⇒c=36/b
inlocuim in relatia ac=24
18/bx36/b=24
648/b²=24
24b²=648
b²=648/24
b²=27
b=√27
b=3√3
a=18/b=18/3√3=6/√3=rationalizam=6√3/3=2√3
a=2√3
c=36/b=36/3√3=12/√3=12√3/3=4√3
c=4√3