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

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Answer 1 · 2018-06-24T12:15:36

# A= +- B #

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 #

Answer 2 · 2018-06-24T12:17:50

Cross multiply

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

as above