Answer:
[tex]\sqrt{85}[/tex]
Step-by-step explanation:
Given
x - [tex]\frac{1}{x}[/tex] = 9 ← square both sides
(x - [tex]\frac{1}{x}[/tex])² = 9²
x² - 2 + [tex]\frac{1}{x^2}[/tex] = 81 ( add 2 to both sides )
x² + [tex]\frac{1}{x^2}[/tex] = 83
Now
(x + [tex]\frac{1}{x}[/tex])² = x² + [tex]\frac{1}{x^2}[/tex] + 2, thus
x² + [tex]\frac{1}{x^2}[/tex] = 83 + 2 = 85
(x + [tex]\frac{1}{x}[/tex] )²= 85 ( take the square root of both sides)
x + [tex]\frac{1}{x}[/tex] = [tex]\sqrt{85}[/tex]
