Question

raportul dintre numerele naturale x si y este de 4/9 .Media geometrica a celor 2 numere este de 48
a) Afla numerele a si b
b)Calculati media aritmetica a celor doua numere.

Answer 1

x/y=4/9
=> x=4k
=> y=9k

a)
Mg=48
√x•y=48
√4k•9k=48
√36k²=48
6k=48
k=8
=> x=4•8=48
=> y=9•8=72

b)
Ma=(x+y)/2
Ma=(48+72)/2
Ma=120/2
Ma=60

Answer 2

$\frac{x}{y} = \frac{4}{9}$⇒9x=4y
[tex] \sqrt{x*y} =48 [/tex]
$\sqrt{x*9x} =48$
$(\sqrt{x*9x} ) ^{2} =48 ^{2}$
$9x ^{2} =2304$
x²=2304:9
x²=256
$x= \sqrt{256}$
x=16

9x=4y
9*16=4y
4y=144
y=144/4
y=36

M=(x+y):2=?
M=(16+36):2=26