SOLUTION: Find all integers k such that the trinomial is a perfect square trinomial
64x(squared) + kxy + y (squared)
So am I just replacing k ?
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64x(squared) + kxy + y (squared)
So am I just replacing k ?
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Question 686945: Find all integers k such that the trinomial is a perfect square trinomial
64x(squared) + kxy + y (squared)
So am I just replacing k ? Found 3 solutions by MathLover1, stanbon, Edwin McCravy:Answer by MathLover1(20849) (Show Source):
You can put this solution on YOUR website!
Perfect Square Trinomials: These are of the form
given:
....using a Rule for the Square of a Sum (a + b) ^2 = a ^2 + 2ab + b ^2, where and we can find
and it is
You can put this solution on YOUR website! Find all integers k such that the trinomial is a perfect square trinomial
64x(squared) + kxy + y (squared)
So am I just replacing k ?
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Yes, solve for "k":
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Your Problem:
(8x)^2 + kxy + y^2
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Perfect Square Form: a^2 + 2ab + b^2
Your Problem:
a = 8x ; b = y
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Middle term has to be 2ab = 2(8x)y = 16xy
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So k has to be 16
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Cheers,
Stan H.
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The other tutors did not mention that there are two answers.
The problem did not state that k must be a POSITIVE integer. It
just stated that k must be an integer, and an integer can be
POSITIVE or NEGATIVE. So we must give both answers.
If 64x² + kxy + y²
is a perfect square it will have to factor as
either (8x + y)² or as (8x - y)²
If it factors as (8x + y)², then that is the same as
(8x + y)(8x + y) = 64x² + 16xy + y². In that case the
middle term +kxy would equal to +16xy and so k would be 16.
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If it factors as (8x - y)², then that is the same as
(8x - y)(8x - y) = 64x² - 16xy + y². In that case the
middle term +kxy would equal to -16xy and so k would be -16.
Answer: Two possibilities: k = 16, k = -16
Edwin
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