“Mathematics, rightly viewed, possesses not only truth, but supreme beauty” Bertrand Russell
Compute in (less than) 30 seconds without using calculator.
My technique:
Since 2007 is the arithmetic mean of the numbers 2004, 2006, 2008 and 2010, then: Let x = 2007
So, x-3 = 2004, x-1 = 2006, x+1 = 2008, x+3 = 2010
Hence, the expression is equal to
Simplifying,
= x2 – 5 = (2007)2 – 5 = 4, 028, 044
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Physics undergraduate student in Manila, Philippines
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I happend to stumble on your 11:59 P.M. 29 December 2008 blog entry and was reminded of a similar algebraic manipulation I came up with back in August 2008 (and have since learned is rather standard, at least in late 1800s texts). Follow the URL I pasted in the ‘Website’ window.