Question

the difference of two natural no is 5 and and the difference of their recipocals is 5/14 ​

Answer 1

HOPING THIS WILL HELP YOU PLZ MARK AS BRAINLIEST AND FOLLOW ME

Answer 2

Answer:

$\bigstar{\bold{The\:numbers\:are\:2\:and\:7}}$

Step-by-step explanation:

$\Large{\underline{\underline{\sf{Given:}}}}$

• Difference of two natural numbers is 5
• Difference of their reciprocals is 5/14

$\Large{\underline{\underline{\sf{To\:Find:}}}}$

• The numbers

$\Large{\underline{\underline{\sf{Solution:}}}}$

➤ Let the first number be x

➤ Let the second number be y

➤ By given,

    x - y = 5

    x = 5 + y-------(1)

➤ The reciprocal of the two numbers is given by,

➤ Reciprocal of first number = 1/x

➤ Reciprocal of second number = 1/y

➤ By given,

    1/x - 1/y = 5/14

➤ Substitute the value of x from first equation,

    1/(5 + y) - 1/y = 5/14

➤ Cross multiplying,

     $\sf{\dfrac{5+y-y}{5y+y^{2} }=\dfrac{5}{14} }$

➤ Again cross multiplying,

    70 = 25y + 5y²

➤ Dividing whole equation by 5

    14 = 5y + y²

    y² + 5y - 14  = 0

➤ Factorising by splitting the middle term

   y² + 7y - 2y - 14 = 0

   y (y + 7) - 2 (y + 7) = 0

   (y + 7) ( y - 2) = 0

➤ y + 7 = 0

    y = -7

➤ This cannot happen as the numbers are natural numbers

➤ y - 2 = 0

    y = 2

➤ Hence the value of y is 2

➤ Substitute the value of y in equation 1

    x  = 5 + 2

    x = 7

➤ Hence the value of x is 7

➤ Therefore the numbers are 2 and 7

    $\boxed{\bold{The\:numbers\:are\:2\:and\:7}}$

$\Large{\underline{\underline{\sf{Verification:}}}}$

➤ x - y = 5

   7 - 2 = 5

   5 = 5

➤ 1/x - 1/y = 5/14

    1/7 - 1/2 = 5/14

    (7 - 2)/14 = 5/14

    5/14 = 5/14

➤ Hence verified.