The sum of two natural numbers is 15 and the sum of their reciprocals is 1/2. Find the numbers. plzz only fast brainlist answer.
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the sum of two natural numbers
a + b = 15 ------------------- (1)
sum of their reciprocals
1/a + 1/b = 1/2
(a + b) / ab = 1/2
ab = 2 ( a+b) = 2 x 15
= 30
(a-b)^2 = (a+b)^2 - 4 x ab
= 15 x 15 - 4 x 30
= 225 - 120
= 105
a - b = sq.root of 105 = 10.25 (appr.)
so. a-b = 10.25 ------------------------- (2)
a+ b = 15 --------------------------- (1)
(1) + (2)
2 a = 25.25
a = 12.625
b = 15 - 12.625
= 2.375
a + b = 15 ------------------- (1)
sum of their reciprocals
1/a + 1/b = 1/2
(a + b) / ab = 1/2
ab = 2 ( a+b) = 2 x 15
= 30
(a-b)^2 = (a+b)^2 - 4 x ab
= 15 x 15 - 4 x 30
= 225 - 120
= 105
a - b = sq.root of 105 = 10.25 (appr.)
so. a-b = 10.25 ------------------------- (2)
a+ b = 15 --------------------------- (1)
(1) + (2)
2 a = 25.25
a = 12.625
b = 15 - 12.625
= 2.375
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