Question

Efectuati: (2-√3)³= ; (√2-√3)³= ; (3√5+1)³= ; (2+√3)³= ;

Answer 1

$(2- \sqrt{3} )^{3} = (2- \sqrt{3} ) (2- \sqrt{3} ) (2- \sqrt{3} ) = (4- 2\sqrt{3} - 2\sqrt{3} +3) (2- \sqrt{3} )$ = $(7-4 \sqrt{3} ) (2- \sqrt{x3} )=14-7 \sqrt{3} -8 \sqrt{3} +12=26-15 \sqrt{3}$
$( \sqrt{2}- \sqrt{3} )^{3} =( \sqrt{2}- \sqrt{3} )( \sqrt{2}- \sqrt{3} )( \sqrt{2}- \sqrt{3} )=(2- \sqrt{6}- \sqrt{6} +3 )*$$( \sqrt{2}- \sqrt{3})=(5-2 \sqrt{6} )( \sqrt{2}- \sqrt{3} )=5 \sqrt{2}-5 \sqrt{3}-2 \sqrt{12}_2 \sqrt{ 3^{2}*2}=$$5 \sqrt{2}-5 \sqrt{3}-4 \sqrt{3}+6 \sqrt{2}=11 \sqrt{2}-9 \sqrt{3}$
$(3 \sqrt{5}+1)^{3}=(3 \sqrt{5}+1)(3 \sqrt{5}+1)(3 \sqrt{5}+1)=(45+3 \sqrt{5}+3 \sqrt{5}+1)*$$(3 \sqrt{5}+1)=(46+6 \sqrt{5})(3 \sqrt{5}+1)=138 \sqrt{5}+46+18 \sqrt{5}+6 \sqrt{5}=46+$$162 \sqrt{5}$
$(2+ \sqrt{3})^{3}=(2+ \sqrt{3})(2+ \sqrt{3})(2+ \sqrt{3})=(4+2 \sqrt{3}+2 \sqrt{3}+3)(2+ \sqrt{3})$=$(7+4 \sqrt{3})(2+ \sqrt{3})=14+7 \sqrt{3}+8 \sqrt{3}+12=26+15 \sqrt{3}$