Problem
ALG-B1-M03-P005 A Reciprocal Expression
#5
★☆☆☆☆ Level 1 of 5
Let \(x\ne0\) and \(x+\frac1x=5\). Find \(x^2+\frac1{x^2}\).
Square the equality.
\(\left(x+\frac1x\right)^2=x^2+2+\frac1{x^2}=25\).
Hence \(x^2+\frac1{x^2}=23\).
A basic example of reciprocal substitution.