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If x = 3 + √8, find the value of x\(\frac{1}{x^2}\) .

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Given that x = 3 + √ 8

And given to find the value of x2\(\frac{1}{x^2}\)

We have x = 3 + √ 8

The rationalising factor for denominator is 3 - √ 8

Also, (x + \(\frac{1}{x^2}\)) = 3 + √ 8 + 3 - √ 8 = 3 + 3 = 6

 (x + \(\frac{1}{x^2}\)) = 6

We know that,

by putting x + \(\frac{1}{x^2}\) = 6 in the above we get,

= 36 - 2 = 34 

The value of x2\(\frac{1}{x^2}\) is 34.

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