Two-numbers-differ-by-6-The-sum-of-their-reciprocals-is-2-15-Determine-the-numbers-

Question Number 217064 by ArshadS last updated on 28/Feb/25

Two numbers differ by 6 . The sum of their reciprocals is \frac{2}{15} .

D e t e r m i n e t h e n u m b e r s .

Answered by A5T last updated on 28/Feb/25

\frac{1}{a} + \frac{1}{b} = \frac{2}{15} \Rightarrow 15 (a + b) = 2 ab

a - b = \underline{+} 6 \Rightarrow a = b \underline{+} 6

a = b + 6 \Rightarrow 15 (b + 3) = b (b + 6)

\Rightarrow b^{2} - 9 b - 45 = 0 \Rightarrow b = \frac{9 \underline{+} \sqrt{261}}{2}

\Rightarrow a = \frac{21 \underline{+} \sqrt{261}}{2} \Rightarrow (a, b) = (\frac{21 \underline{+} \sqrt{261}}{2}, \frac{9 \underline{+} \sqrt{261}}{2})

a = b - 6 \Rightarrow 15 (b - 3) = b (b - 6)

\Rightarrow b^{2} - 21 b + 45 b = 0 \Rightarrow b = \frac{21 \underline{+} \sqrt{261}}{2} \Rightarrow a = \frac{9 \underline{+} \sqrt{261}}{2}

Commented by ArshadS last updated on 28/Feb/25

Thanks sir!

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