#### Solve: If x = 5 – 2√6, find 1/x, (x^{2} – 1/x^{2})

**Solution:**

Given:

x = 5 – 2√6

so,

1/x = 1/(5 – 2√6)

**By rationalizing the denominator,**

1/(5 – 2√6) = [1(5 + 2√6)] / [(5 – 2√6) (5 + 2√6)]

= [(5 + 2√6)] / [5^{2} – (2√6)^{2}]

= [(5 + 2√6)] / [25 – 4.6]

= [(5 + 2√6)] / [25 – 24]

= (5 + 2√6)

Then,

x + 1/x = 5 – 2√6 + (5 + 2√6)

= 10

**Square on both sides we get**

(x + 1/x)^{2} = 10^{2}

x^{2} + 1/x^{2} + 2x.1/x = 100

x^{2} + 1/x^{2} + 2 = 100

x^{2} + 1/x^{2} = 100 – 2

= 98

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