Answer: 8 and [tex]\frac{1}{8}[/tex]
Step-by-step explanation:
x + [tex]\frac{1}{x}[/tex] = [tex]\frac{65}{8}[/tex]
need to eliminate the denominator:
x(8x) + [tex]\frac{1}{x}[/tex](8x) = [tex]\frac{65}{8}[/tex](8x)
8x² + 8 = 65x
8x² - 65x + 8 = 0
(8x -1)(x - 8) = 0
(8x -1) = 0 (x - 8) = 0
x = [tex]\frac{1}{8}[/tex] x = 8
