Question

[tex](1+ \sqrt{5- \sqrt{3} } )(1- \sqrt{5- \sqrt{3} } )+(1- \sqrt{7+ \sqrt{3} } )( 1+\sqrt{7+ \sqrt{3} } )
[/tex]
A,0
B.-11
C.-10
D.4

Answer 1

Poti folosi formula de calcul prescurtat: (a+b)(a-b) = a² - b²

$(1+\sqrt{5-\sqrt{3}})(1-\sqrt{5-\sqrt{3}}) = 1^2-(\sqrt{5-\sqrt{3}})^2 = 1 - (5-\sqrt{3})$
$(1+\sqrt{7+\sqrt{3}})(1-\sqrt{7+\sqrt{3}}) = 1^2-(\sqrt{7+\sqrt{3}})^2 = 1 - (7+\sqrt{3})$

$1-(5-\sqrt{3})+1-(7+\sqrt{3}) = 2 - 5 - 7 + \sqrt{3} - \sqrt{3} = -10$

Solutie: -10.

Answer 2

Buna!
$(1+ \sqrt{5- \sqrt{3} } )(1- \sqrt{5- \sqrt{3} } )+(1- \sqrt{7+ \sqrt{3} } )( 1+\sqrt{7+ \sqrt{3} } )$  =
1 - ( 5-√3 ) + 1 - ( 7+√3 ) =
1-5+√3+1-7-√3 =
-10 ( C )

Bafta :)