Question

Compute

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

Answer 1

We could use:


`(a-b)(a+b)=a^2-b^2`

For the first and third factors there will be:


`(√(3755)+√(3752))(√(3755)-√(3752))=(√(3755))^2-(√(3752))^2=\\\\3755-3752=3`

and for the second and fourth:


`(-√(3755)-√(3752))(√(3752)-√(3755))=\\\\= (-√(3755)-√(3752))(-√(3755)+√(3752))=\\\\= (-√(3755))^2-(√(3752))^2=3755-3752=3`

So the answer is:


`3\cdot 3=\boxed{9}`