Question

The sum of two numbers is 15 if the sum of reciprocal is 3/10 do. Find numbers

Answer 1

» Sum of two numbers is 15.

Let two numbers be M and N.

=> M + N = 15 ______ (eq 1)

=> M = 15 - N _______ (eq 2)

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» The sum of their reciprocal is $\frac{3}{10}$

=> $\dfrac{1}{M}$ + $\dfrac{1}{N}$ = $\dfrac{3}{10}$

=> $\dfrac{N\:+\:M}{MN}$ = $\dfrac{3}{10}$

=> $\dfrac{15}{MN}$ = $\dfrac{3}{10}$

=> $\dfrac{5}{MN}$ = $\dfrac{1}{10}$

=> 50 = NM

=> 50 = N (15 - N)

=> 50 = 15N - N²

=> N² - 15N + 50 = 0

=> N² - 10N - 5N + 50 = 0

=> N(N - 10) -5(N - 10) = 0

=> (N - 5) (N - 10) = 0

• N - 5 = 0

=> N = 5 _____ (eq 3)

• N - 10 = 0

=> N = 10 _____ (eq 4)

» Put value of (eq 3) in (eq 2)

=> M = 15 - 5

=> M = 10

» Put value of (eq 4) in (eq 2)

=> M = 15 - 10

=> M = 5

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Numbers are : 5 and 10

__________ [ANSWER]

Answer 2

Answer:

let numbers be x and y

x+y =15

1/x+1/y=3/10

x+y/xy=3/10

15/xy=3/10

xy= 50

as product is 50 and sum is 15 so numbers are 5 and 10

Step-by-step explanation: