Question

(√27-2)(2-3√3)

(5√3+√27):√3

(√5-1)^2-(2√5+1)^2

Answer 1

$(sqrt{27}-2)(2-3sqrt{3})=(3sqrt{3}-2)(2-3sqrt{3})=- (2-3sqrt{3})(2-3sqrt{3})=-(2-3sqrt{3})^2=\ =-(4-12sqrt{3}+27)=-(31-12sqrt{3})=12sqrt{3}-31$

$frac{5sqrt{3}+sqrt{27}}{sqrt{3}}=frac{5sqrt{3}+3sqrt{3}}{sqrt{3}}=frac{8sqrt{3}}{sqrt{3}}=8$

$(sqrt{5}-1)^2-(2sqrt{5}+1)^2=((sqrt{5}-1)-(2sqrt{5}+1))((sqrt{5}-1)+(2sqrt{5}+1))=\ =(sqrt{5}-1-2sqrt{5}-1))(sqrt{5}-1+2sqrt{5}+1)=(-sqrt{5}-2)*3sqrt{5}=-15-6sqrt{5}$
можно и по другому
$(sqrt{5}-1)^2-(2sqrt{5}+1)^2=5-2sqrt{5}+1-(20+4sqrt{5}+1)=5-2sqrt{5}+1-20-4sqrt{5}-1=\ =-15-6sqrt{5}$