Question

radical din (2p+1)³+√(2p-1)³ / √4p+2radical din 4p²-1    precizez ca numitorul este totul sub radical

Answer 1

$\frac{ \sqrt{(2p+1)^3} + \sqrt{(2p-1)^3} }{ \sqrt{4p+2 \sqrt{4p^2-1} } } =$

$=\frac{[\sqrt{(2p+1)} +\sqrt{(2p-1)}] [\sqrt{(2p+1)}^2 +\sqrt{(2p-1)}^2-\sqrt{(2p+1)} *\sqrt{(2p-1)}] }{ \sqrt{ (2p+1)+ (2p-1) +2 \sqrt{(2p+1)(2p-1)} } }=$

$=\frac{[\sqrt{(2p+1)} +\sqrt{(2p-1)}] [4p-\sqrt{(4p^2-1)} ] }{ \sqrt{[ \sqrt{(2p+1)} +\sqrt{(2p-1)} ]^2 } } =$

$=\frac{[\sqrt{(2p+1)} +\sqrt{(2p-1)}] [4p-\sqrt{(4p^2-1)} ] }{ [\sqrt{(2p+1)} +\sqrt{(2p-1)} ]} =$

$=4p-\sqrt{(4p^2-1)}$