Question

The arithmetic mean of two numbers is 18. Their geometric mean is 16. Find the sum of the squares of the two numbers.

Answer 1

arthemtic mean is \[(x+y)\div2\]=18
and geometric mean is xy=16
solve these equations for x and y

Answer 2

what does it mean by the sum of the two squares?

Answer 3

the sum of the two squares basically means that the sum of the two numbers after they have been squared.

Answer 4

so far I have \[a+b=36\] & \[ab=256\]

my teacher said that the geometric mean is\[\sqrt{ab}\]

Answer 5

hey sry its \[\sqrt{xy}\]

Answer 6

they mean \[x^{2}+y^{2}\]

Answer 7

then u have a+b square it

Answer 8

it will be \[a^{2}+b^{2}+2ab\]

Answer 9

use ur values to obtain solution

Answer 10

\[\left( 36 \right) \left( a^2+512+b^2 \right)\] is this the right equation?

Answer 11

[36^{2}=a^{2}+b^{2}+512\]

Answer 12

therefore, \[a^2+b^2=784\]

Answer 13

haa....thats all
hope u understood the solutionn

Answer 14

Yes, thank you so much!