SOLUTION: Can someone please help me sum of two consecutive integers is 19 less than their product. find the integers. 1st 1st or 2nd 2nd

Algebra ->  Conversion and Units of Measurement -> SOLUTION: Can someone please help me sum of two consecutive integers is 19 less than their product. find the integers. 1st 1st or 2nd 2nd      Log On


   

Question 405164: Can someone please help me sum of two consecutive integers is 19 less than their product. find the integers. 1st 1st or 2nd 2nd
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let two integers be x and y
if we have two consecutive integers, then x and y=x%2B1

their sum is 19 less than their product, so
x+%2B+%28x%2B1%29+%2B+19+=+x%28x%2B1%29.....solve for x
2x%2B20+=+x%5E2%2Bx
0+=+x%5E2%2Bx+-2x+-20
0+=+x%5E2+-x+-20
+x%5E2+-x+-20=0.....find roots if a=1,b=+-1 and c=+-20

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A1%2A%28-20%29+%29%29%2F%282%2A1%29+

x+=+%281+%2B-+sqrt%28+1%2B80+%29%29%2F2+

x+=+%281+%2B-+sqrt%28+81+%29%29%2F2+

x+=+%281+%2B-+9%29%2F2+

x1+=+%281+%2B+9%29%2F2+=10%2F2=5
x2+=+%281+-+9%29%2F2+=-8%2F2=-4
now find
%28x1%2B1%29=5%2B1=6
%28x2%2B1%29=-4%2B1=-3
so, you have two pairs of consecutive numbers:
first pair: x=5,and %28x%2B1%29=6
second pair:x=-4, and %28x%2B1%29=-3




check:
x+%2B+%28x%2B1%29+%2B+19+=+x%28x%2B1%29
5%2B+%285%2B1%29+%2B+19+=+5%285%2B1%29
5%2B+6+%2B+19+=+30
30+=+30

or, other pair
x+%2B+%28x%2B1%29+%2B+19+=+x%28x%2B1%29
-4%2B+%28-3%29+%2B+19+=+-4%28-3%29
-7+%2B+19+=+12
12+=+12