Math, asked by anita9696, 11 months ago

The sum of two numbers is 16.The sum of their reciproclas is 1/3.Find the numbers

Answers

Answered by rishu6845

Answer:

12 , 4

Step-by-step explanation:

Let numbers be a and b

ATQ , Sum of two numbers = 16

=> a + b = 16

=> b = 16 - a

Sum of nubers , reciprocals = 1 / 3

=> 1 / a + 1 / b = 1 / 3

=> ( a + b ) / ab = 1 / 3

=> 16 / ab = 1 / 3

=> ab = 48

Putting b = 16 - a in it we get

=> a ( 16 - a ) = 48

=> 16a - a² = 48

=> - a² + 16a - 48 = 0

=> a² - 16a + 48 = 0

=> a² - ( 12 + 4 ) + 48 = 0

=> a² - 12a - 4a + 48 = 0

=> a ( a - 12 ) - 4 ( a - 12 ) = 0

=> ( a - 12 ) ( a - 4 ) = 0

If a - 12 = 0

=> a = 12

b = 16 - a = 16 - 12 = 4

If a - 4 = 0

=> a = 4

b = 16 - a = 16 - 4 = 12

So numbers are 12 and 4

Answered by Aɾꜱɦ

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