(1) sum of the rational roots of the equation.

x⁵ = (133x-78)/ 133-78x

how can i solve this question.

x^5 = (133x-78)/ 133-78x



133x^5 - 78x^6 = 133x - 78



78x^6 - 133x^5 + 133x - 78=0



sum of roots = (-1)^1 -b/a = 133/78

hope it helps..cheero:)

he asked for the sum of rational roots only

Notice that if

 is a root so is  

 (Admin Sir, could you kindly see that the latex output comes inline with the text)

Both 1 and -1 are roots of the equation (That the product of roots is -1 also tells us that -1 is necessarily is a root)

Now 

(Since we have already noted that  are roots)

and since the reciprocal is also a root we must also have

This means if x is a real root, then

Now from rational roots theorem if x is a rational root of the equation, then

where p and q are both integer divisors of 78.

Here the real roots are positive. The factors of 78 to be considered are 1,2, 3, 6, 13, 26,39, 78

You can easily see that none of the fractions formed by these numbersother than   satisfy the condition mentioned above. A quick check reveals that  and hence  are roots

Hence the rational roots are ,  and

Hence the sum of rational roots is

Are there some issues with the editor or is it just me.

When I try to edit the post, several extra spacings come in which makes the post unreadable.

Also, what is the criterion for locking the edit? I came back to the post half-an-hour later and I am not able to remove the spacings.

I may be making some mistake in formatting, so I would appreciate it if someone pointed it to me.

Thanx