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

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      Log On


   

Question 1012698: 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
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!




Multiply the first equation through by w4 and the second one through by w8

matrix%281%2C3%2C1%2F%28a+b+c+d%29+=+2w%5E6%2C%22%2C%22%2C+1%2F%28a+b+c+d+%29+=+2w%5E9+%29

Things equal to the same thing are equal to each other, so

matrix%281%2C3%2C2w%5E6%2C%22%22=%22%22%2C+2w%5E9+%29

Divide both sides by 2w6

matrix%281%2C3%2C1%2C%22%22=%22%22%2C+w%5E3+%29

The only real number solution is w = 1

Substituting in the original
(1)


or



Edwin