Question

Can someone please help me with this question? I came up with a completely different answer. I will show you my steps down below. I will medal the person with the best answer. Thanks!

Calculate the geometric mean of 5 and 125.

25
12.5
17.7
20

Answer 1

5/125=125/x 5x=15625 x=3125

Answer 2

if x is the geometric mean, then you must have
\(\huge \dfrac{5}{x}=\dfrac{x}{125}\)

Answer 3

Oh, it should be

\[\large \frac{5}{x} = \frac{x}{125}\]

Answer 4

Then cross multiply and solve for 'x'

Answer 5

note that you will get 2 geometric means.
only one is in the choices

Answer 6

Okay so, x^2=625

Answer 7

so x =25

Answer 8

yes
what are the 2 values of x ?

Answer 9

x=25 and ?

Answer 10

and 25 is the one which is in the choices :)

Answer 11

How do I find a second value? That doesn't make sense. I thought there was only one value.

Answer 12

\[\large x^2 = 625\]
\[\large x = \pm 25\] :)

Answer 13

\(x^2 =a^2 \implies x =\pm a\)

Answer 14

always remember that x^2 means its a quadratic equation, and x must have 2 values

Answer 15

example :
x^2 =100
gives x= 10 , -10
because (-10)^2 also = 100

Answer 16

so it's -25?

Answer 17

its 25, -25
and 25 is in the choices

Answer 18

Okay thanks! You have been very helpful.

Answer 19

welcome :)