Question

the sum of reciproral of two consecutive positive integers is 17/72. find the integers​

Answer 1

$\large \underline{ \underline{ \sf \: Solution : \: \: \: }}$

Let ,

$\to$

The two consecutive positive integers be x and x + 1

By the given condition ,

$\implies \sf \frac{1}{x} + \frac{1}{(x + 1)} = \frac{17}{72} \\ \\ \implies \sf \frac{(x + 1) + (x)}{x(x + 1)} = \frac{17}{72} \\ \\ \implies \sf \frac{2x + 1}{ {x}^{2} + x} = \frac{17}{72} \\ \\ \implies \sf 144x + 72 = 17 {x}^{2} + 17x \\ \\ \implies \sf \star \: by \: prime \:factorisation \: method \\ \\ \implies \sf 17 {x}^{2} - 127x - 72 = 0 \\ \\ \implies \sf 17 {x}^{2} - 136x + 9x- 72 = 0 \\ \\ \implies \sf 17x(x - 8) + 9(x - 8) = 0 \\ \\ \implies \sf (17x + 9)(x - 8) = 0 \\ \\ \implies \sf x = - \frac{9}{17} \: \: or \: \: x = 8$

Therefore , the required positive integers -9/17 and 8/17 or 8 and 9

Answer 2

Answer:

8 and 9

Step-by-step explanation:

go through the attachment and hope u will make out the sum