Expert: David Hemmer - 10/8/2008

Question
Hello - a friend of mine posed a math equation to me as a challenge since he couldn't solve it.  I tried every logarithm and convergence trick I know and still came up empty.

Can this equation be solved for "y" using only laws of math and not by a computer program:

x = (y^-1) + (y^-2) + (y^-3) + (y^-4) +(y^-5)



thanks,
Dave

Answer
no it can't. Consider the function:

f(t)=1/t + 1/t^2 +1/t^3 + 1/t^4 +1/t^5

You are aksing if the function can be solved for t. At a minimum this would require the function to be invertible. However:

f'(t)=-1/t^2-2/t^3-3/t^4-4/t^5-5/t^6

Check that f'(2) is around -3.94 while

f'(9) is positive. Thus f is decreasing for a while then increasing, it is not invertible. You can't solve for t with a computer or any other "laws of math".