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प्रश्न
The sum of two number a and b is 15, and the sum of their reciprocals `1/a` and `1/b` is 3/10. Find the numbers a and b.
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उत्तर
Given that a and b be two numbers in such a way that b = (15 - a).
Then according to question
`1/a+1/b=3/10`
`(b + a)/(ab)=3/10`
`(a + b)/(ab)=3/10`
By cross multiplication
10a + 10b = 3ab ........ (1)
Now putting the value of b in equation (1)
10a + 10(15 - a) = 3a(15 - a)
10a + 150 - 10a = 45a - 3a2
150 = 45a - 3a2
3a2 - 45a + 150 = 0
3(a2 - 15a + 50) = 0
(a2 - 15a + 50) = 0
a2 - 10a - 5a + 50 = 0
a(a - 10) - 5(a - 10) = 0
(a - 10)(a - 5) = 0
a - 10 = 0
a = 10
Or
a - 5 = 0
a = 5
Therefore,
When a = 10 then
b = 15 - a = 15 - 10 = 5
And when a = 5 then
b = 15 - a = 15 - 5 = 10
Thus, two consecutive number be either a = 5, b = 10 or a = 10, b = 5.
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