SOLUTION: I honestly can not make sense of this word problem. I do not know how to start it. The sum of the squares of two consecutive odd integers is 67 more than the larger of the two int

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: I honestly can not make sense of this word problem. I do not know how to start it. The sum of the squares of two consecutive odd integers is 67 more than the larger of the two int      Log On


   



Question 1156634: I honestly can not make sense of this word problem. I do not know how to start it.
The sum of the squares of two consecutive odd integers is 67 more than the larger of the two integers. What are the two integers?
I honestly think I write it this way: x+(x+2)=67+(x+2)

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I read it this way:
+x%5E2+%2B+%28+x+%2B+2+%29%5E2+=+x+%2B+2+%2B+67+
+x%5E2+%2B+x%5E2+%2B+4x+%2B+4+=+x+%2B+69+
+2x%5E2+%2B+3x+-+65+=+0+
-----------------------------
Use quadratic formula:
+x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+2+
+b+=+3+
+c+=+-65+
+x+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A2%2A%28-65%29+%29%29%2F%282%2A2%29+
+x+=+%28-3+%2B-+sqrt%28+9+%2B+520+%29%29+%2F+4+
+x+=+%28-3+%2B-+sqrt%28+529+%29%29+%2F+4+
+x+=+%28+-3+%2B+23+%29+%2F+4+
+x+=+20%2F4+
+x+=+5+
and
+x+=+%28+-3+-+23+%29+%2F+4+ ( can't use the negative solution )
---------------------
The consecutive odd integers are: 5 and 7
--------------------
check:
+x%5E2+%2B+%28+x+%2B+2+%29%5E2+=+x+%2B+2+%2B+67+
+5%5E2+%2B+%28+5+%2B+2+%29%5E2+=+5+%2B+2+%2B+67+
+25+%2B+49+=+74+
+74+=+74+
OK