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))