Find two consecutive odd integers who's product is 195

Question

Find two consecutive odd integers who's product is 195

Answer 1

x and x+2 are the integers

x(x+2)=195

x²+2x=195

x²+2x-195=0

195=3*5*13 and 3*5=15, 15-13=2 the coefficient of the middle term

factor

(x+15)(x-13)=0

x-13=0

x=13

x+2=15

13*15=195

using only arithmetic...

find the square root of 195

√195=13.964

use the whole number part of the square root, 13

13+2=15

13 and 15 again