Given that x - y = a and xy = b , show that x^2 + y^2 = a^2 + 2b .

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18-08-2016
Mathematics

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Given that x - y = a and xy = b , show that x^2 + y^2 = a^2 + 2b .

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caylus caylus · Answer 1 · 2016-08-18T16:29:03+02:00

caylus caylus

18-08-2016

Hello,

[tex]x-y=a ==\textgreater \ (x-y)^2=a^2 \ ==\textgreater \ x^2-2xy+y^2=a^2\\\\ xy=b\ ==\textgreater\ 2xy=2b\\\\ x^2-2xy+b^2+2xy=a^2+2b==\textgreater\ x^2+y^2=a^2+2b [/tex]

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