Determine for which values of x, √(2x^(2)-1)/x=x will have no roots?

1 Answer
Mar 30, 2018

x= +-1

Explanation:

sqrt(2x^(2)-1)/x=x
sqrt(2x^(2)-1)= x^2
2x^(2)-1 = (x^2)^2

Let x^2 = m
2m - 1 = m^2
m^2 - 2m + 1 = 0
m = +-1

x^2 = m
x^2 = -1 => no real solutions
x^2 = 1 => x= +-1 and both values works in the original equation:

Check:
sqrt(2xx1^(2)-1)/1=1
sqrt(2xx(-1)^(2)-1)/-1=-1