JAMB - Mathematics (2012 - No. 7)
Simplify \((\sqrt{6} + 2)^2 - (\sqrt{6} - 2)^2\)
\(2\sqrt{6}\)
\(4\sqrt{6}\)
\(8\sqrt{6}\)
\(16\sqrt{6}\)
Explicação
\((\sqrt{6} + 2)^2 - (\sqrt{6} - 2)^2\)
= \([(\sqrt{6} + 2) + (\sqrt{6} - 2)][(\sqrt{6} + 2) - (\sqrt{6} - 2)]\)
= \((\sqrt{6} + 2 + \sqrt{6} - 2)(\sqrt{6} + 2 - \sqrt{6} + 2)]\)
= \((2\sqrt{6})(4)\)
= \(8\sqrt{6}\)
= \([(\sqrt{6} + 2) + (\sqrt{6} - 2)][(\sqrt{6} + 2) - (\sqrt{6} - 2)]\)
= \((\sqrt{6} + 2 + \sqrt{6} - 2)(\sqrt{6} + 2 - \sqrt{6} + 2)]\)
= \((2\sqrt{6})(4)\)
= \(8\sqrt{6}\)