The sum of a number and its reciprocal is 3 by 41 /80
Answers
Answer:
Let the number be x.
Therefore the reciprocal = 1/x
Therefore x + 1/x = 3 41/80 = 281/80
x + 1/x = x² + 1 = 281/80
x
Cross multiply 281x = 80x² + 80
Therefore:
80x² - 281x + 80 = 0
Expand the equation
80x² - 256x - 25x + 80 = 0
16x(5x - 16) - 5(5x - 16) = 0
(16x - 5) (5x - 16) = 0
Therefore:
16x - 5 = 0 or 5x - 16 = 0
16x = 5 or 5x = 16
16x = 5 , hence x = 5/16
or
5x = 16, hence x = 3 1/5 (3 and 1/5)
Therefore x = 5/16 or 16/5
Step-by-step explanation:
Let the number be x.
Therefore the reciprocal = 1/x
Therefore x + 1/x = 3 41/80 = 281/80
x + 1/x = x² + 1 = 281/80
Cross multiply 281x = 80x² + 80
Therefore:
80x² - 281x + 80 = 0
Expand the equation
80x² - 256x - 25x + 80 = 0
16x(5x - 16) - 5(5x - 16) = 0
(16x - 5) (5x - 16) = 0
Therefore:
16x - 5 = 0 or 5x - 16 = 0
16x = 5 or 5x = 16
16x = 5 , hence x = 5/16
Therefore,5/16 or 16/5