The sum of two numbers is 8and the sum of their reciprocals is 8/15 find the numbers
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let a and b are two numbers ,
according to question,
a + b = 8 -------(1)
1/ a + 1/b =8/15
=> ( a + b)/ab =8/15
from equation (1)
8 /ab = 8/15
ab = 15
now,
equation (1)
a + b = 8
take square both side
a^2 +b^2 + 2ab = 64
(a -b)^2 +4ab =64
( a -b)^2 =64 -4ab =64 -4 × 15 =4
take square root
(a - b) = +_2
now ,
solve by use ,
(a -b) = +_ 2
& (a +b) =2
if (a -b) =2 then a =5 , and b =3
if ( a-b) = -2 then a =3 and b =5
according to question,
a + b = 8 -------(1)
1/ a + 1/b =8/15
=> ( a + b)/ab =8/15
from equation (1)
8 /ab = 8/15
ab = 15
now,
equation (1)
a + b = 8
take square both side
a^2 +b^2 + 2ab = 64
(a -b)^2 +4ab =64
( a -b)^2 =64 -4ab =64 -4 × 15 =4
take square root
(a - b) = +_2
now ,
solve by use ,
(a -b) = +_ 2
& (a +b) =2
if (a -b) =2 then a =5 , and b =3
if ( a-b) = -2 then a =3 and b =5
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