1986 AIME Problems/Problem 2: Difference between revisions

Revision as of 18:04, 4 July 2013

Evaluate the product $(\sqrt 5+\sqrt6+\sqrt7)(-\sqrt 5+\sqrt6+\sqrt7)(\sqrt 5-\sqrt6+\sqrt7)(\sqrt 5+\sqrt6-\sqrt7)$ .

Simplify by repeated application of the difference of squares.

$\left((\sqrt{6} + \sqrt{7})^2 - \sqrt{5}^2\right)\left(\sqrt{5}^2 - (\sqrt{6} - \sqrt{7})^2\right)$

$= (13 + 2\sqrt{42} - 5)(5 - (13 - 2\sqrt{42}))$

$= (2\sqrt{42} + 8)(2\sqrt{42} - 8)$

$= (2\sqrt{42})^2 - 8^2 = 104$

Revision as of 13:38, 6 May 2007 view source I_like_pie (talk \| contribs) 446 edits →See also ← Older edit		Revision as of 18:04, 4 July 2013 view source Nathan wailes (talk \| contribs) 2,960 edits No edit summary Newer edit →
Line 17:		Line 17:

	[[Category:Intermediate Algebra Problems]]		[[Category:Intermediate Algebra Problems]]
			{{MAA Notice}}

1986 AIME (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15
All AIME Problems and Solutions