How do you solve #\frac { 1} { x } = \frac { x } { 9}#?

Question

418 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-02T07:13:54

#x = 3" "# or #" "x = -3#

Use the difference of squares identity:

#a^2-b^2 = (a-b)(a+b)#

with #a = x# and #b = 3# as follows:

Given:

#1/x = x/9#

Multiply both sides by #x# to get:

#1 = x^2/9#

Multiply both sides by #9# to get:

#9 = x^2#

Subtract #9# from both sides to get:

#0 = x^2-9 = x^2-3^2 = (x-3)(x+3)#

So:

#x = 3" "# or #" "x = -3#