The sum of two numbers is 16.The sum of their reciproclas is 1/3.Find the numbers
Answers
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
12,4
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