Question

Media geometrica a numerelor a si b este egala cu 4√5.
Daca a=7-3√5, determinati numarul b si media aritmetica a numerelor a si b.

Answer 1

√a×b=4√5
√[(7-3√5)×b]=4√5
ridicam la patrat
(7-3√5) × b= 16×5
(7-3√5) × b= 80
b=80/(7-3√5)
b=80(7+3√5)/(7-3√5)(7-3√5)
b=80(7+3√5)/(49-45)
b=80(7+3√5)/4
b=20(7+3√5)
b=140+60√5

ma=(7-3√5+140+60√5)/2=(147+57√5)/2=73,5+28,5√5

verificare
√(140+60√5)(7-3√5)=
=√(980+420√5-420√5-900)=
=√80=4√5