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Answer on Algebra Question for jojo alex

Question #4925
the sum of 2 numbers is 16 the sum of their reciprocals is 1/3 find the number ?
Expert's answer
Solution
We have two unknown numbers and two conditions on these numbers.
Let's designate these numbers through x , y.
Let's make system of the equations.

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Let's solve system of the equations.
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data:image/png;base64,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
data:image/png;base64,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
Thus
data:image/png;base64,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 or data:image/png;base64,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
data:image/png;base64,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
Answer: These numbers are 4 and 12.

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Comments

jayashree
01.11.2011 06:12

a+b=16
1/a+1/b=1/3
ab=48
a*(16-a)=48
a2-16a+48=0
a2-12a-4a+48=0
a(a-12)-4(a-12)=0
a=4,12

ihsan
31.10.2011 16:34

the numbers are following
1st number = 4
2nd number = 12

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