Question

The sum of two number a and b is 15 and the sum of their recrprocals 1/a and 1/b is 3/10 find the number of a and b

Answer 1

we know that , (a+b) = 15
and 1/a + 1/b = 3/10

so , in 1/a + 1/b = 3/10

=> if we make denominator equal ,

=> (b+a)/ab = 3/10


=> 15/ab = 3/10

=> 1/ab = 3/10 × 1/15

=> 1/ab = 1/50

=> ab = 50


=> b = 50/a

(a+b) = 15

=> a + 50/a = 15 (substitute value of b in a+b = 15)

=> (a²+50)/a = 15

=> a² + 50 = 15 a

=> 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
=> a-5 = 0 => a= 5


if a = 10 then , b = 50/a = 50/10 = 5

& if a = 5 then , b= 50/a = 50/5 = 10


so , a and b both can be 5 or 10


hope this helps