how to prove x+xy+t+y
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We have that
x2=y2⟺x2−y2=0⟺(x−y)(x+y)=0
Now we can conclude that either x−y=0 (so that x=y) or x+y=0 (so that x=−y). Hence, if x2=y2, it is true that x=±y.
The reverse is immediate.
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