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If (a+b)^2 =2a^2+2b^2 prove that a=b

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Posted by Sandra Fernandes 8 years, 4 months ago

Rashmi Bajpayee 8 years, 4 months ago

{tex}{\left( {a + b} \right)^2} = 2{a^2} + 2{b^2}{/tex}

=> {tex}{a^2} + {b^2} + 2ab = 2{a^2} + 2{b^2}{/tex}

=> {tex}2ab = {a^2} + {b^2}{/tex}

=> {tex}{a^2} + {b^2} - 2ab = 0{/tex}

=> {tex}{\left( {a - b} \right)^2} = 0{/tex}

=> {tex}a-b=0{/tex}

=> {tex}a=b{/tex}

Hence proved

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