Math, asked by ravitmg3, 1 year ago

The sum of two number 12 if the sum of their reciprocal is 3 upon fine the number

Answers

Answered by Shubhendu8898
0

Let that  two numbers  be  x and  y

According  to question,

Sum of  numbers  = 12

x + y = 12

y = 12 - x  .......................i)

And,

Sum  of  their  reciprocal = 3

\frac{1}{x}+\frac{1}{y}=5


Putting  y = 12 -x,


\frac{1}{x}+\frac{1}{12-x}=\frac{3}{5}\\\;\\\frac{12-x+x}{x(12-x)}=\frac{3}{5}\\\;\\\frac{12}{12x-x^{2}}=\frac{3}{5}\\\;\\\frac{4}{12x=x^{2}}=\frac{1}{5}\\\;\\12x-x^{2}=20\\\;\\12x-x^{2}-20=0\\\;\\x^{2}-12x+20\\\;\\x^{2}-10x-2x+20\\\;\\x(x-10)-2(x-10)\\\;\\(x-2)(x-10)\\\;\\x=2\;\;or\;\;x=10


Hence,

Numbers are  10 and  2

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