1.

The sum of two numbers is 15. Sum of its reciprocals is 3/10. Find the numbers.

Answer»

Let x, 15 – x be the numbers

\(\frac{1}{x}+\frac{1}{15-x}=\frac{3}{10}\)

\(\frac{15-x+x}{15x-x^2}=\frac{3}{10}\)

150 = 45x - 3x2

3x2 - 45x + 150 = 0

x2 - 15x + 50 = 0

\(x=\frac{-15\pm \sqrt{225-200}}{2}=\frac{15\,\pm\,5}{2}=10,5\)

Numbers = 10, 5



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