Using only p&p, determine the simplest fractional form of this expression:
3333373 - 3333263
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3333373 + 6666633
(333337^3 - 333326^3)/(333337^3 + (6666663)^3)
Note1 333337 = (1/3(1000000+11)
Note2 333326 = (1/3(1000000-22)
Note3 666663 = (1/3(2000000-11) = 333337+333326
(1/3(1000000+11)^3)^3-((1/3(1000000-22))^3))/(((1/3(1000000+11)))^3+((1/3(2000000-11)))^3
Cancel ((1000000+11)^3 - (1000000-22)^3)/((1000000+11)^3+(2000000-11)^3)
Let 1000000=x, to save ink, let 11=y
Factor the top: ((x+y))^3-((x-2y)^3) = 9y(x^2-xy+y^2)
Factor the bottom (((x+y))^3+((2x-y))^3 = 9x(x^2-xy+y^2)
Cancel 9y/9x, or y/x
Substitute y/x=11/1000000, a solution I'm sure has delighted generations of homework markers!
Edited on September 4, 2023, 9:16 am
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Posted by broll
on 2023-09-04 09:07:28 |
Possible Solution
