If \(x+\frac{1}{x}=7\), then what is the value of \(x^{2}+\frac{1}{x^{2}} + 1\)?
x + 1/x = 7 square both sides
(x + 1x) (x + 1/x) = 49
x^2 + x (1/x) + x (1/x) + 1/x^2 = 49
x^2 + 1 + 1 + 1/x^2 = 49 subtract 1 from both sides and rearrange the left side
x^2 + 1/x^2 + 1 = 48 Voila !!!!
+1206 
