Question

bạn bạn thân yêu ơi,Giu1p mik giải câu toán này trong hôm nay nhé!Mai mik phải nộp r!:))

(\(4+\sqrt{15}\))(\(\sqrt{10}-\sqrt{6}\))\(\sqrt{4-\sqrt{15}}\)

Cảm ơn các bạn rất nhiều!:)))Ciao!Arigato!Gracias!,...:))))

Answer 1

\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}=\left(4+\sqrt{15}\right)\left(\sqrt{5}-\sqrt{3}\right)\sqrt{2}.\sqrt{4-\sqrt{15}}=\left(4+\sqrt{15}\right)\left(\sqrt{5}-\sqrt{3}\right)\sqrt{8-2\sqrt{15}}=\left(4+\sqrt{15}\right)\left(\sqrt{5}-\sqrt{3}\right)\sqrt{5-2.\sqrt{5}.\sqrt{3}+3}=\left(4+\sqrt{15}\right)\left(\sqrt{5}-\sqrt{3}\right)\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}=\left(4+\sqrt{15}\right)\left(\sqrt{5}-\sqrt{3}\right)\text{|}\sqrt{5}-\sqrt{3}\text{|}=\left(4+\sqrt{15}\right)\left(\sqrt{5}-\sqrt{3}\right)^2=\left(4+\sqrt{15}\right)\left(8-2\sqrt{15}\right)=\left(4+\sqrt{15}\right)\left(4-\sqrt{15}\right).2=\left(16-15\right).2=2\)