#A/B=B/A" "# is true if?

2 Answers
Jun 24, 2018

# A= +- B #

Explanation:

If #A/B = B/A# then (assuming #A,B != 0#) multiplying by #AB# we get:

#A/B * AB = B/A * AB#

# :. A^2 = B^2#

# :. A^2 - B^2 = 0#

# :. (A-B)(A+B)= 0#

# { (A-B= 0=> A=B), (A+B= 0=> A=-B) :} #

Thus there are two possibilities

# A= +- B #

Jun 24, 2018

Cross multiply

#A/B=B/A" is true if "A^2=B^2" in which case "A=+-B#

Explanation:

as above