Question

The sum of two number is 18.the sum of their reciprocals is 1/4.find the value
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Answer 1

Answer:

x + y= 18......(ii)

1/x + 1/y= 1/4

(x + y)/ xy= 1/4

Substituting value of (x+y) in (ii) in the above equation,

xy =4*18=72

y=72/x......(i)

Substituting value of (i) in ( ii)

x + 72/x =18

x^2-18x-72=0

(x-6)(x-12)=0

When x=6

Substituting value of x in (i), y=12

When x=12

Substituting value of x in (i), y=6

So we have 2 answers,

Either x=6,y=12 or x=12,y=6