If (x^2+1) / x = 7 find x^2 + (1/x^2)

x² + (1/x²) = 47

Step-by-step explanation:

by identity : (a+b) ² = a²+b²+2ab

(x+1/x) ² = x² + (1/x) ²+2 (x) (1/x)

(x+1/x) ² = x² + (1/x²) + 2 ... (1)

since : (x²+1) / x = 7

(x²/x) + (1/x) = 7

x + (1/x) = 7

put the value for : x + (1/x) in (1):

49 = x² + (1/x²) + 2

x² + (1/x²) = 47