If k:k^2+1::k^2:k+1 for a real k then number of values of k are

M4maths Previous Puzzles

02 Jan 2013 variable k

If k:k^2+1::k^2:k+1 for a real k
then number of values of k are

OPtion

1) 0
2) 1
3) 2
4) 3
5) 4
6) none of these

Solution

on solving this we get
k(k+1) = k^2(k^2+1)
so k[k(k^2+1)-(k+1)] = 0
so k[k^3-1] = 0
so k[k-1][k^2+k+1] = 0
so real roots are 0 and 1

Correct Option: 3 Best Solution (0)