+0  
 
0
64
4
avatar

How many solutions does the equation \( \frac{(x-1)(x-2)(x-3)\dotsm(x-100)}{(x-1^2)(x-2^2)(x-3^2)\dotsm(x-100^2)} = 0\) have for \(x\)?

 Feb 20, 2021
 #1
avatar+944 
+1

The equation simplifies to:

 

\((x-1)(x-2)(x-3) \dots (x-100) = 0\)

 

There are 100 solutions, namely x = 1 to x = 100.

 Feb 20, 2021
 #2
avatar
0

I don't think it does.

I'm pretty sure the constant is squared and not the whole thing.

So like \((x-1)(x-4)(x-9)...(x-10000)\)

 Feb 20, 2021
 #3
avatar
0

So can someone else help?

Guest Feb 20, 2021
 #4
avatar+118069 
+1

Note  that  x  cannot   be   any perfect  square  from  x =  1  to  x = 100  (i.e.,  x= 1^2  to x = 10^2)  because  any  of  these  make  the  denominator  = 0

 

So......we  only  have   90   possible   x values  for  the  numerator 

 

 

cool cool cool 

 Feb 20, 2021

15 Online Users

avatar
avatar