If x + 1/x = 4 , find the value of x^2 + 1/x^2 .

14. Squaring both sides: (x + 1/x )^2 = x^2 + 2 + 1/x^2 = 16 , so x^2 + 1/x^2 = 16 - 2 = 14 .

If $x + \frac{1}{x} = 4$ , find the value of $x^{2} + \frac{1}{x ^{2}}$ .

Competition practiceAlgebra

Squaring both sides:

(x + \frac{1}{x})^{2} = x^{2} + 2 + \frac{1}{x ^{2}} = 16

, so

x^{2} + \frac{1}{x ^{2}} = 16 - 2 = 14

Answer: D) 14

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