Question

А) (√5-1)(√5+1) Б) (√5-1)(√5+2) в) (√5+2)^2 г) (√5+2)(√5+1) - (√5-2)(√5-1)

Answer 1

$(a-b)*(a+b) = a^2-b^2\A\ ( sqrt{5} - 1) *( sqrt{5}+1 ) = 5 - 1 = 4\B\( sqrt{5} - 1) *( sqrt{5}+2 ) = ( sqrt{5} - 1) *( (sqrt{5}+1) + 1 ) = 5 - 1 + sqrt{5} - 1= sqrt{5} +3$
$C\( sqrt{5}+2 )^2 = 5 + 4 +4* sqrt{5}  = 9 + 4* sqrt{5}$
$D\ ( sqrt{5}+2 )*( sqrt{5}+1 )-( sqrt{5}-2 )*( sqrt{5}-1 ) =(( sqrt{5}+1) +1)*( sqrt{5}+1 )-(( sqrt{5}-1) -1)*( sqrt{5}-1 ) = ( sqrt{5}+1 )^2 + ( sqrt{5}+1 ) - ( sqrt{5}-1)^2+( sqrt{5}-1) = 6* sqrt{5}$