SOLUTION: The sum of a and b is 132. If a is the square of b and the product of a and b is negative, what is a?

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Question 1119835: The sum of a and b is 132. If a is the square of b and the product of a and b is negative, what is a?
Found 2 solutions by greenestamps, rothauserc:
Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


Given:
(1) a%2Bb+=+132
(2) a+=+b%5E2

Then
b%5E2%2Bb+=+132
b%5E2%2Bb-132+=+0
%28b%2B12%29%28b-11%29+=+0
b+=+-12 or b+=+11

If b = -12 and a+b = 132, then a = 144; then ab = -1728.

If b = 11 and a+b = 132, then a = 121; then ab = 1331.

Since the problem specifies that the product ab is negative, then b must be -12 and a is 144.

Answer: a = 144

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
a + b = 132
:
a = b^2
:
b^2 +b -132 = 0
:
(b-11) * (b+12) = 0
:
b = 11 and b = -12
:
a * b < 0 implies that b < 0
:
b = -12
:
therefore
:
a = b^2 = (-12)^2 = 144
: