Question

The sum of 2 numbers a and b is 15 and the sum of their reciprocal 1 upon a and 1 upon b is 3 upon 10 find the value of a and b

Answer 1

$a + b = 15 \\ so \: a = 15 - b\\ \frac{1}{a} + \frac{1}{b} = \frac{3}{10} \\ cross \: multiply \: the \: second \: equation \\ \frac{(b + a)}{ab} = \frac{3}{10} \\ \frac{15}{ab} = \frac{3}{10} \\ ab = \frac{15 \times 10}{3} \\ ab = 50 \\ (15 - b)b = 50 \\ 15b - {b}^{2} = 50 \\ {b}^{2} - 15b + 50 = 0 \\ {b}^{2} - 10b - 5b + 50 = 0 \\ b(b - 10) - 5(b - 10) = 0 \\ (b - 10)(b - 5) = 0 \\ so \: the \: numbers \: are{10 \:and \: 5}$