Preparation for math olympiad UKMT junior senior intermediate maths challenge smc jmc imc 2022 2023

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Isn't it simpler if you said at the begining that a^2-b^2=0 and a×b=0 ( make a system ) and then had a=0/b=0 and b=0/a =0 ?
(I'm not sure it is correct)

Ps: the video was awesome and nicely explained👍

bobcatpg