Question

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

Answer 1

Sol:
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 - x ) = 3/10
150 = 45x - 3x
3x - 45x + 150 = 0
x - 15x + 50 = 0
(x - 10)(x - 5) = 0
x = 10 or 5
Therefore, the numbers are 10 and 5.
If x = 15

Answer 2

let one number be x, then other is 15-x
(1/x)+(1/15-x)=3/10
by lcm,
(15-x+x)/(x)(15-x)=3/10
15*10=3(x)(15-x)
30=x(15-x)
x²-15x+30=0
x=[15±√(15²-4*30)]÷2
x=[15±√5]÷2