Question

the sum of two number is 15 if sum of their reciprocal is 3 upon 10 . find the number

Answer 1

Let one of the numbers be x.

Other number is (15 - x)

Sum of their reciprocals = 3/10

1/x + 1/(15 - x) = 3/10

(15 ) / (15x - x2) = 3/10

150 = 45x - 3x2

3x2 - 45x + 150 = 0

x2 - 15x + 50 = 0

(x - 10)(x - 5) = 0

x = 10 or 5

Therefore, the numbers are 10 and 5.

If x = 15

Hope this helps!

Answer 2

$\huge\mathfrak{Heya}$

$\mathsf{Let \ the \ one \ number \ be \ x.}$

$\mathsf{Then \ the \ other \ number \ will \ be \ 15 - x.}$

$\mathsf{A/q}$

$\mathsf{1/x+ 1/(15 - x) = 3/10}$

$\mathsf{[15 - x + x]/[(x)(15 - x)}] = 3/10$

$\mathsf{15x - x^2 = 50}$

$\mathsf{x^2 - 15x + 50 = 0}$

$\mathsf{x^2 - 10x - 5x + 50}$

$\mathsf{x(x - 10) - 5(x - 10) = 0}$

$\mathsf{(x - 10)(x - 5) = 0}$

$\mathsf{x = 10, 5}$

$\mathsf{Case \ I \ :-}$

$\mathsf{When \ x = 10}$

$\mathsf{15 - x = 15 - 10 = 5}$

$\mathsf{Case \ II \ :-}$

$\mathsf{When \ x = 5}$

$\mathsf{15 - x = 15 - 5 = 10}$

$\mathsf{So, \ the \ numbers \ are \ 10 \ and \ 15.}$

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$\mathsf{Hope \ this \ helps \ you.}$