Question

a) (1-√3)²+(1+√3)²-(1-√3)(1+√3)=...
b) (2√5+√2)²-(2√5-√2)²+(2√5+√2)(2√5-√2)=...
Dar va rog pe lug sa explicat clar ☺

Answer 1

     
$a)\,\,\, (1- \sqrt{3})^{2}+(1+ \sqrt{3})^{2}-(1-\sqrt{3})(1+\sqrt{3})= \\ =(1-2\sqrt{3}+3)+(1+2\sqrt{3}+3)-( 1^{2} - ( \sqrt{3} )^{2})= \\ =(4-2\sqrt{3})+(4+2\sqrt{3})-( 1 - 3)= \\ =4-2\sqrt{3}+4+2\sqrt{3}-( - 2)= \\ =4+4+2=10$ 


$b)\,\,\, (2 \sqrt{5} + \sqrt{2})^{2}-(2 \sqrt{5} - \sqrt{2})^{2}+(2 \sqrt{5} + \sqrt{2})(2 \sqrt{5} - \sqrt{2})= \\ =(20 + 4 \sqrt{10}+2)-(20-4 \sqrt{10}+2)+ ((2 \sqrt{5})^{2}-( \sqrt{2})^{2})= \\ =(22 + 4 \sqrt{10})-(22-4 \sqrt{10})+ (20-4)= \\ = 22 + 4\sqrt{10}-22+4\sqrt{10}+ 16= \\ =16+8\sqrt{10} = 8(2+\sqrt{10})$