EXPLANATION.
⇒ x = 3 + √8.
As we know that,
We can write expression as,
⇒ 1/x = 1/(3 + √8).
Rationalizes the equation into middle term splits, we get.
⇒ 1/x = 1/(3 + √8) x [(3 - √8)/(3 - √8)].
⇒ 1/x = [(3 - √8)/(3 + √8)(3 - √8)].
⇒ 1/x = [(3 - √8)]/[(3)² - (√8)²].
⇒ 1/x = [(3 - √8)]/[9 - 8].
⇒ 1/x = (3 - √8).
To prove : (x² + 1/x²) = 34.
As we know that,
Formula of :
⇒ (a + b)² = a² + b² + 2ab.
Using this formula in this question, we get.
⇒ (x + 1/x)² = (x)² + (1/x)² + 2(x)(1/x).
⇒ [3 + √8 + 3 - √8]² = x² + 1/x² + 2.
⇒ (3 + 3)² = x² + 1/x² + 2.
⇒ (6)² = x² + 1/x² + 2.
⇒ 36 = x² + 1/x² + 2.
⇒ x² + 1/x² = 36 - 2.
⇒ x² + 1/x² = 34.
∴ Hence proved.
