Maths Olympiad Prep

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Algebra Difficulty 4.8 AIME Find the answer

Example 8. Calculate (5+6+7)(5(\sqrt{5}+\sqrt{6}+\sqrt{7})(\sqrt{5}
+67)(56+7)(5+6+7). \begin{array}{l} +\sqrt{6}-\sqrt{7})(\sqrt{5}-\sqrt{6}+\sqrt{7}) \\ \cdot(-\sqrt{5}+\sqrt{6}+\sqrt{7}) . \end{array}

A number or a short expression. Spacing and $ signs are ignored.

Solution

Analyze the repeated application of the difference of squares formula to get the result as 104.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.