The product of two consecutive integers is 380. How do you find the integers?

Jul 14, 2016

There are 2 such pairs: (-20;-19) and (19;20)

Explanation:

To find the numbers we have to solve the equation :

$n \times \left(n + 1\right) = 380$

${n}^{2} + n - 380 = 0$

$\Delta = 1 - 4 \times 1 \times \left(- 380\right)$

$\Delta = 1521$

$\sqrt{\Delta} = 39$

${n}_{1} = \frac{- 1 - 39}{2} = - 20$

${n}_{2} = \frac{- 1 + 39}{2} = 19$

Now the solutions are: n_1=-20;n_1+1=-19 and n_2=19;n_2+1=20