JAMB 1990 · UME · Q19

If $x + \dfrac1x = 4$ , find $x^2 + \dfrac{1}{x^2}$ .

Worked solution (try it first)

Square both sides of $x + \dfrac1x = 4$ .
The middle term is $2 \times x \times \frac1x = 2$ , so $x^2 + 2 + \dfrac{1}{x^2} = 16$ .
Subtract 2: $x^2 + \dfrac{1}{x^2} = 14$ , option B.