Question

if x is equal to 5 - 2 underroot 6
$find {x }^{2} + \frac{1}{x} {}^{2}$
​

Answer 1

Answer:

x²+1/x² = 98

Explanation:

Given x = 5-2√6 ---(1)

1/x = 1/(5-2√6)

=(5+2√6)/[(5-2√6)(5+2√6)]

= (5+2√6)/[5²-(2√6)²]

= (5+2√6)/(25-24)

= 5+2√6 ---(2)

Now ,

x +1/x

= 5-2√6+5+2√6

= 10 ----(3)

x²+1/x² = (x+1/x)²-2

= (10)² - 2

= 100 - 2

= 98

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