the sum of two number is 15 and sum of its reciprocal is 3/ 10 .find the numbers.
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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 - 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
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
Answered by
0
let two numbers be x and 15-x
1/x + 1/15-x = 3/10
1/x + 1/15-x = 3/10
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