What I understand is you are trying to square these terms and arrive at an equation which is of the nature x^4, which leads you to believe that it has 4 roots. However, that is not always the case, any equation of the nature x^n will have n roots, but for these to be real it would have to satisfy some condition. If it does not then the roots are imaginary. That applies to the expression you get. However I am not sure what that condition is for an expression of the 4th order.

Hope this helps.

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rkatl wrote:

btw, the explaination given for the above problem is

This equation has no roots. sqrt(x^2 + 1) is bigger than or equal to 1, sqrt(x^2 + 2) is bigger than or equal to sqrt(2). Therefore, sqrt(x^2 + 1) + sqrt(x^2 + 2) is bigger than or equal to 1 + sqrt(2), which is bigger than 2.

I can't seem to understand this logic.