Question

1/x+1/y=1/z xy=z, what is the average of x and y?

Answer 1

so u have 1/x+1/y=1/z
what to do ?

Answer 2

hmm

Answer 3

flying x method?

Answer 4

that gives me x+y/xy=1/z

Answer 5

does this make sense :
(x+y)/xy = 1/z ..........

Answer 6

u are fast!

Answer 7

flying x method for addition

Answer 8

I got that method out of a 1985 SAT book I think...

Answer 9

I don't know if they till teach it anymore...

Answer 10

now u have xy = z, so put it there

Answer 11

still

Answer 12

k...

Answer 13

(x+y)/z = 1/z
what u get ?

Answer 14

k

Answer 15

zx+zy/xy

Answer 16

wait

Answer 17

got to put movie for my mom

Answer 18

can't u just cancel z from both sides ?

Answer 19

I'm back

Answer 20

k

Answer 21

we can cancel x and y

Answer 22

to get z+z I think

Answer 23

so

Answer 24

zx+zy/xy=2z

Answer 25

no!
\(\large \frac{x+y}{z}=\frac{1}{z} \implies x+y=1\)
got this ?

Answer 26

multiplying z on both sides..

Answer 27

so wait a minute

Answer 28

x+y/xy

Answer 29

x+y/xy=1/z

Answer 30

put xy=z

Answer 31

ahh

Answer 32

sometimes I forget to convert...

Answer 33

k

Answer 34

got it

Answer 35

x+y=1

Answer 36

so the average of x and y is 1/2

Answer 37

so what's average?

Answer 38

1/2

Answer 39

yup :)