Question

Выполните действия: а) (√3-√5)^2
б) (2√7+1)^2
в) (2-√3)^3
г) (3√5+1)^3

Answer 1

$(apm b)^2=a^2pm2ab+b^2 \ (apm b)^3=a^3pm 3a^2b+3ab^2pm b^3$

$(sqrt{3}-sqrt{5})^2=(sqrt{3})^2-2 cdotsqrt{3}cdot sqrt{5}+(sqrt{5})^2=3-2 sqrt{15}+5=8-2 sqrt{15} \ (2sqrt{7}+1)^2=(2sqrt{7})^2+2cdot2sqrt{7}cdot1+1^2=28+4sqrt{7}+1=29+4sqrt{7} \ (2- sqrt{3} )^3=2^3-3cdot2^2cdot sqrt{3} +3cdot2cdot ( sqrt{3} )^2-( sqrt{3} )^3= \ =8-12sqrt{3}+18-3sqrt{3}=26-15 sqrt{3} \ (3sqrt{5} +1)^3=(3sqrt{5})^3+3cdot(3sqrt{5})^2cdot1+3cdot3sqrt{5}cdot1^2+1^3= \ =135 sqrt{5}+135+9 sqrt{5} +1=144sqrt{5}+136$