Question Number 10157 by ketto last updated on 27/Jan/17

the difference of two number is 3.  if the sum of their reciprocal is   (7/(10)) . find the numbres

Answered by FilupSmith last updated on 28/Jan/17

a−b=3    ⇒    a=3+b  (1/a)+(1/b)=(7/(10))  ((a+b)/(ab))=(7/(10))  ((3+b+b)/((3+b)b))=(7/(10))  ((3+2b)/(3b+b^2 ))=(7/(10))  10(3+2b)=7(3b+b^2 )  30+20b=21b+7b^2   7b^2 +b−30=0  b=((−1±(√(1+840)))/(14))  b=((−1±29)/(14))  b =    2,    −((15)/7)     a=3+b  ∴ a=5, (3−((15)/7))