Question 1203032
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<pre>

We write  4x^2 - kx + 81 = {{{(ax+b)^2}}}.


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.
</pre>

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.