Given, 8a−5b8c−5d=8a+5b8c+5d
⇒ 8a−5b8a+5b=8c−5d8c+5d [Applying alternendo]
8a−5b+8a+5b8a−5b−8a−5b=8c−5d+8c+5d8c−5d−8c−5d [Applying componendo and dividendo]
16a−10b=16c−10d
ab=cd
Hence, the above statement is true.
If 8a−5b8c−5d=8a+5b8c+5d, then ab=cd