[tex]\Big(1+\sqrt{5-\sqrt3}\Big)\Big(1-\sqrt{5-\sqrt3}\Big)+ \Big(1-\sqrt{7+\sqrt3}\Big)\Big(1+\sqrt{7+\sqrt3}\Big)= \\ \\ =1^2-\Big(\sqrt{5-\sqrt3}\Big) ^ 2 + 1^2-\Big(\sqrt{7+\sqrt3}\Big)^2 = \\ \\ = 1-|5-\sqrt3|+1-|7+\sqrt3| = 1-(5-\sqrt3)+1-(7+\sqrt3) = \\ \\ = 1-5+\sqrt3+1 -7-\sqrt3= \\ \\= 2-12 = -10 \\ \\ \\ $M-am folosit de formula: \quad (a-b)(a+b) = a^2-$b$^2[/tex]
