Question

The sum of the two numbers a and b is 15 and the x sum of their reciprocals 1/a and 1/b is 3/10. Find the numbers a and b

Answer 1

there you go

given

a+b=15 ......(1)

1/a+1/b= 3/10

a+b/ab= 3/10

using vaue of a+b from (1) we have;

15/ab= 3/10

ab=15*10/3

ab=50

therefore a=50/b .....(2)

from (1)

a+b=15

50/b+ b= 15 (substitued value of a from (2))

50+b^2/b=15

50+b^2=15b

b^2-15b+50=0

b^2-10b-5b+50=0

(b-10)(b-5)=0

b=10,5

a=50/b

a=5,10

therefore if a=5 b=10

a=10 b=5

hope it helps

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