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Compute

$(\sqrt{3755}+\sqrt{3752})(-\sqrt{3755}-\sqrt{3752})(\sqrt{3755}-\sqrt{3752})(\sqrt{3752}-\sqrt{3755})$.
Thanks!

Respuesta :

WojtekR
We could use:

[tex](a-b)(a+b)=a^2-b^2[/tex]

For the first and third factors there will be:

[tex](\sqrt{3755}+\sqrt{3752})(\sqrt{3755}-\sqrt{3752})=(\sqrt{3755})^2-(\sqrt{3752})^2=\\\\3755-3752=3[/tex]

and for the second and fourth:

[tex](-\sqrt{3755}-\sqrt{3752})(\sqrt{3752}-\sqrt{3755})=\\\\= (-\sqrt{3755}-\sqrt{3752})(-\sqrt{3755}+\sqrt{3752})=\\\\= (-\sqrt{3755})^2-(\sqrt{3752})^2=3755-3752=3[/tex]

So the answer is:

[tex]3\cdot 3=\boxed{9}[/tex]

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