How many solutions in real numbers does the equation

(√3-1)x = 2(√2+1)x + 1

have?

The LHS (without the power) is <1, and so the entire LHS is a monotonically decreasing function of x.  By similar analysis, the RHS is a monotonically increasing function of x.  A quick plot shows that the plots cross for a value of x where -1.5<x<-1.4 

Posted by Kenny M on 2025-01-10 11:12:53