Question

Aratati ca : (√5+√3)·radical mai lung din 4-√15=√2

Answer 1

radicalul mai lung il scoti conform formulei apoi imnultesti $\sqrt{4- \sqrt{15} } = \sqrt{ \frac{4+ \sqrt{16-15} }{2} } - \sqrt{ \frac{4- \sqrt{16-15} }{2} } = \sqrt{ \frac{5}{2} } - \sqrt{ \frac{3}{2} } = \frac{ \sqrt{5}- \sqrt{3} }{ \sqrt{2} }$$( \sqrt{5} + \sqrt{3} )( \frac{ \sqrt{5}- \sqrt{3} }{ \sqrt{2} } )= \frac{ \sqrt{5} ^{2}- \sqrt{3} ^{2} }{ \sqrt{2} } = \frac{2}{ \sqrt{2} } = \frac{2 \sqrt{2} }{2} = \sqrt{2}$
cat m-am chinuit sa scriu ,as merita o bere