Question

find number of real solution :
(x-1)²+(x-2)²+(x-3)²+.................+(x-2013)² = 0​

Answer 1

Answer:

(x−1)  

2

+(x−2)  

2  +.............+(x−n)  2  =0

clearly this is a quadratic equation equation equation since all the terms are quadratic.

Now, we know square of any term is always non-negative .

Therefore,

This equation will never cross x-axis that is it will always be greater than zero.

The parabola graphically will never cross x-axis and hence there will be no real solution.

Hence, the answer zero.