the sum of 2 number is 8 and the sum of their reciprocals is 8/15. Find the numbers
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here is the answer to your question
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Let us suppose the two numbers to be x and y..
According To the Question,
x+y=8 =>x=8-y..(1)
1/x+1/y=8/15
Putting the value of (1) in the above equation, we get..
1/(8-y)+1/y=8/15
y+8-y/(8-y)(y)=8/15
On cross multiplying..
8y^2-64y+120=0
y^2-8y+15=0
y^2-5y-3y+15=0
y(y-5)-3(y-5)=0
(y-3)(y-5)=0
y=3, y=5...
Putting this in (1) we get,
( x=5, x=3 )
Thank You !
According To the Question,
x+y=8 =>x=8-y..(1)
1/x+1/y=8/15
Putting the value of (1) in the above equation, we get..
1/(8-y)+1/y=8/15
y+8-y/(8-y)(y)=8/15
On cross multiplying..
8y^2-64y+120=0
y^2-8y+15=0
y^2-5y-3y+15=0
y(y-5)-3(y-5)=0
(y-3)(y-5)=0
y=3, y=5...
Putting this in (1) we get,
( x=5, x=3 )
Thank You !
nandana12:
Txz
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