Question

The sum of two numbers is 15 and the sum of their reciprocal is 3/10. Find the numbers.

Answer 1

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Answer 2

let the numbers be x and y

x+y= 15......(1)

1/x+1/y=3/10

x+y/xy=3/10

15/xy=3/10

xy=50.........(2)

((1))².......x²+y²+2xy=(15)²

x²+y²+2(50)=225

x²+y²=125.......(3)

(x-y)²=x²+y²-2xy=125-2(58)=125-100=25

(x-y)²=25

x-y=5........(4)

(1)+(2).....2x=20 then x=10

x+y=15.......10+y=15........y=5

there fore x=10&y=5