Question 1119835
<br>
Given:
(1) {{{a+b = 132}}}
(2) {{{a = b^2}}}<br>
Then
{{{b^2+b = 132}}}
{{{b^2+b-132 = 0}}}
{{{(b+12)(b-11) = 0}}}
{{{b = -12}}}  or  {{{b = 11}}}<br>
If b = -12 and a+b = 132, then a = 144; then ab = -1728.<br>
If b = 11 and a+b = 132, then a = 121; then ab = 1331.<br>
Since the problem specifies that the product ab is negative, then b must be -12 and a is 144.<br>
Answer: a = 144