Question

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Answer 1

Answer:

$(\sqrt{a} + \sqrt{b} )( \sqrt{a} - \sqrt{b} ) = a - b \\ \\ we \: know \: that \: ( \sqrt{x} + \sqrt{y} )( \sqrt{x} - \sqrt{y}) = x - y \\ \\ hence \\ ( \sqrt{a} + \sqrt{b} )( \sqrt{a} - \sqrt{b} ) = a - b \\ \\ lhs = rhs \: (\: \: proved)$

Answer 2

Answer:

$( \sqrt{a} + \sqrt{b} )( \sqrt{a} - \sqrt{b} ) = a - b \\ \sqrt{a} ( \sqrt{a} - \sqrt{b} ) + \sqrt{b} ( \sqrt{a} - \sqrt{b} ) \\ a - \sqrt{ab} + \sqrt{ab} - b \\ a - b = a - b \\ \\ \\ \\ hence \: proved \: lhs = rhs$

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