the-difference-of-two-number-is-3-if-the-sum-of-their-reciprocal-is-7-10-find-the-numbres-

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

t h e d i f f e r e n c e o f t w o n u m b e r i s 3 .

i f t h e s u m o f t h e i r r e c i p r o c a l i s

\frac{7}{10} . f i n d t h e n u m b r e s

Answered by FilupSmith last updated on 28/Jan/17

a - b = 3 \Rightarrow a = 3 + b

\frac{1}{a} + \frac{1}{b} = \frac{7}{10}

\frac{a + b}{a b} = \frac{7}{10}

\frac{3 + b + b}{(3 + b) b} = \frac{7}{10}

\frac{3 + 2 b}{3 b + b^{2}} = \frac{7}{10}

10 (3 + 2 b) = 7 (3 b + b^{2})

30 + 20 b = 21 b + 7 b^{2}

7 b^{2} + b - 30 = 0

b = \frac{- 1 \pm \sqrt{1 + 840}}{14}

b = \frac{- 1 \pm 29}{14}

b = 2, - \frac{15}{7}

a = 3 + b

∴ a = 5, (3 - \frac{15}{7})