SOLUTION: Split 1406 into two groups so that the number in one group is the square of the number in the other

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: Split 1406 into two groups so that the number in one group is the square of the number in the other       Log On


   

Question 1118631: Split 1406 into two groups so that the number in one group is the square of the number in the other
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
Call one group 'a', then +a%5E2+%2B+a+=+1406+
+a%5E2+%2B+a+-+1406+=+0+
1406 = 38*37:
+%28a+%2B+38%29%28a+-+37%29+=+0+
a = -38 and/or a = 37 (we discard -38 if we assume you are seeking 'partitions' of 1406)
a=37: +a%5E2+=+1369+ and the sum is 1369 + 37 = 1406,
so the answer is +highlight+%28+37+%29+ + +highlight%281369%29+
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