find two consecutive integers whose product is 194 more than their sum.

Question

 find two consecutive integers whose product is 194 more than their sum.

Answer 1

xy= 194 + x+y

x(x+1) = 194 + x+ x+1

x^2 -x -195 = 0

x = 1/2 + (1/2)sqr(1+4(195)) = a non-integer solution

16+15 = 31

16(15) = 240

240-31 = 209

14 +15 = 29

14(15) = 210

210-29 = 181

14.5 + 15.5 = 30

14.5(15.5) = 224.75

224,75 -30 = 194.75

Maybe instead of 194, you meant 209 or 181? then you'd get either 14 and 15 or 15 and 16

Or, 15 and 16 satisfies

15(16) > 194 +15+16

240 > 214

if the product is 209 more than the sum, then it's also 194 more than the sum.

240>194+30

Although that's a strange way to phrase the problem.