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.