Question

The sum of a number and its reciprocal is 101/10. Find the number

Answer 1

Answer:

10

Step-by-step explanation:

Define x:

Let the number be x

The reciprocal of the number = 1/x

Solve x:

The sum is 101/10

x + 1/x = 101/10

Multiply by x through:

x² + 1 = 101x/10

Multiply by 10 through:

10x² + 10 = 101x

Take away 101x from both sides:

10x² - 101x + 10 = 0

Factorise:

(x - 10)(10x - 1) = 0

Solve x:

x = 10 or x = 1/10

⇒ The number is 10 and the reciprocal is 1/10

Answer: The number is 10

Answer 2

Answer:

10 or 1/10

Step-by-step explanation:

Let the number be x

Reciprocal of x = 1/x

According to Question

$x+\frac{1}{x} = \frac{101}{10}$

Multiplying whole equation by 10x

10x² + 10 = 101x

10x² - 101x + 10 = 0

Splitting the middle term

10x² - 100x - x + 10 = 0

10x( x - 10) -1 (x - 10) = 0

( x - 10) ( 10x - 1) = 0

x - 10 = 0               10x - 1 = 0

x = 10                             x = 1/10