Question

The sum of a number and its reciprocal is 4 . what is their difference?

Answer 1

x + 1/x = 4

Squaring both sides

x^2 + 1/x^2 + 2 = 16

x^2 + 1/x^2 = 16 - 2

x^2 + 1/x^2 = 14 - eq. 1

(x - 1/x)^2

= x^2 + 1/x^2 - 2

From eq. 1, we get,

14 - 2 = 12

So,

(x - 1/x)^2 = 12

Square rooting both sides
$x \: - 1 \div x = 2 \sqrt{3}$
Hope it helps :)

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