SOLUTION: 1/(a w) 1/(b w) 1/(c w) 1/(d w)=2w^2 and 1/(a w^2) 1/(b w^2) 1/( c w^2) 1/(d w^2)=2w then prove that 1/(a 1) 1/(b 1) 1/(c 1) 1/(d 1)=2,there is sign of additio

Algebra ->  Square-cubic-other-roots -> SOLUTION: 1/(a w) 1/(b w) 1/(c w) 1/(d w)=2w^2 and 1/(a w^2) 1/(b w^2) 1/( c w^2) 1/(d w^2)=2w then prove that 1/(a 1) 1/(b 1) 1/(c 1) 1/(d 1)=2,there is sign of additio      Log On


   

Question 1012709: 1/(a w) 1/(b w) 1/(c w) 1/(d w)=2w^2 and 1/(a w^2) 1/(b w^2) 1/( c w^2) 1/(d w^2)=2w then prove that 1/(a 1) 1/(b 1) 1/(c 1) 1/(d 1)=2,there is sign of addition in each term where sign is not visible,please do not consider the sign of multiplicatio expect for 2w and 2w^2
Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
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1/(a w) 1/(b w) 1/(c w) 1/(d w)=2w^2 and 1/(a w^2) 1/(b w^2) 1/( c w^2) 1/(d w^2)=2w then prove that 1/(a 1) 1/(b 1) 1/(c 1) 1/(d 1)=2,there is sign of addition in each term where sign is not visible,please do not consider the sign of multiplicatio expect for 2w and 2w^2
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1. Why do not use the conventional signs?


2. What is the first equality? Is it identity? 
   For what values of w is it valid?

3. Same questions for the second equality.

4. If these equalities are valid for w=1, why do not substitute w=1 directly in them?

5. Take the limit at w ---> 1 
   It might be a joke, or might be a solution.