Question

The sum of a fraction and 4 times its reciprocal is 13/3. What is the fraction?

A) 4/3 B) 3/4 C) 5/4 D) 4/5

Answer 1

Answer:

Step-by-step explanation:

let the fraction be of the form x/y and y/x

x/y + 4y/x = 13/3

(x² + 4y²)xy = 13/3

x² + 4y² = 13xy/3

3x² + 12y² - 13xy = 0

3x² - 13xy + 4y² = 0

3x² - xy - 12xy + 4y² = 0

x(3x-y) - 4y(3x-y) = 0

(x-4y)(3x-y) = 0

so,

x = 4y and x = y/3

if x= 4y then the fraction will be 4 and 1/4 which is not equal to 13/3

so we take x =y/3

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