Question 1203032: Determine the value of k such that the trinomial 4x^2-kx+81 is a perfect square (such as (ax+b)^2.
Answer by ikleyn(52903)   (Show Source):
You can put this solution on YOUR website! .
We write 4x^2 - kx + 81 =  .
It gives us 4x^2 - kx + 81 = a^2*x^2 + 2abx + b^2.
From this, we conclude that either
(a) a = 2, b = 9,
or
(b) a = -2, b = 9,
or
(c) a = 2, b = -9
or
(d) a = -2, b = -9.
It gives for "k" two and only two opportunities: either k = 2ab = 36 or k = 2ab = -36.
Solved.
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Be attentive: the problem INCORRECTLY asks about "the value of k",
while a correct question must be "find all possible values of k".
So, the problem's formulation has a huge underwater stone (is a trap),
expecting you will fall in it.
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