1.

Show that if 2 (a2 + b2 ) = (a + b)2 then a = b

Answer»

Given that 2 (a2 + b2 ) = (a + b)2 

To prove a = b 

As 2 (a2 + b2 ) = (a + b)2 

We have 

2a2 + 2b2 = a2 + 2ab + b2

2a2 – a2 + 2b2 – b2 = 2ab 

a2 + b2 = 2ab This is possible only when a = b 

∴ a = b



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