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Question

The sum of two numbers a and b is 15, and the sum of their reciprocals 1aand1bis310 Find the numbers a and b

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Solution

Given: a+b=15
That is a=15-b .... i)
and 1 over a plus 1 over b equals 3 over 10 .... ii)
putting the value of a from equation i) in equation ii) we get,
fraction numerator 1 over denominator 15 minus b end fraction plus 1 over b equals 3 over 10 fraction numerator b plus 15 minus b over denominator b left parenthesis 15 minus b right parenthesis end fraction equals 3 over 10 rightwards double arrow 150 equals 3 b left parenthesis 15 minus b right parenthesis rightwards double arrow 50 equals 15 b minus b squared rightwards double arrow b squared minus 15 b plus 50 equals 0 rightwards double arrow b squared minus 5 b minus 10 b plus 50 equals 0 rightwards double arrow b left parenthesis b minus 5 right parenthesis minus 10 left parenthesis b minus 5 right parenthesis equals 0 rightwards double arrow left parenthesis b minus 10 right parenthesis left parenthesis b minus 5 right parenthesis equals 0 rightwards double arrow b equals 10 space o r space 5

putting the value of b in equation i) we get
a=15-5 or 15-10
rightwards double arrowa=10 or a=5
Therefore the value of a and b are 5 and 10 or 10 and 5.

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