Question

1. If product of two consecutive numbers is 72<br />then find difference of their roots.​

Answer 1

Step-by-step explanation:

let the consecutive numbers be x and x + 1

product of consecutive numbers is 72

$x(x + 1) = 72 \\ {x}^{2} + x = 72 \\ {x}^{2} + x - 72 = 0 \\ {x}^{2} + 9x - 8x - 72 = 0 \\ x(x + 9) - 8(x + 9) = 0 \\ (x + 9)(x - 8) = 0 \\ x + 9 = 0 \: \: x - 8 = 0 \\ x = - 9 \: \: \: \: \: \: \: x = 8$

we take the positive value of x = 8

the required numbers are

x = 8

x + 1 = 8 + 1 = 9

8 and 9 are the required consecutive numbers

difference between their squares = 17

$= {9}^{2} - {8}^{2} \\ = 81 - 64 \\ = 17$

hope you get your answer