Question

The sum of 2 numbers is 15.if the sum of their reciprocals is 3/10 find the numbers

Answer 1

Solution is attached below

Answer 2

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To find : The required number.

Let us assume that required numbers be x and 15-x. Then:-

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

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

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

150 = 3x ( 15 - x )

150 = 45x - 3x²

x² - 15x + 50 = 0

x² - 10x + 5x + 50 = 0    { MIDDLE TERM SPLITTING METHOD ! }

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

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

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

x = 10 or x = 5

ATLAST, THE TWO REQUIRED NUMBERS ARE :-

TWO NUMBERS = 10 AND 5.