Algebra question

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264

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If (ax + b)(bx + a) = 6x^2 + __ x + 6, where a, b and __ are distinct integers, what is the minumum possible value of __ , the coefficient of x?

$\phantom{26x^2, 26}$

$\phantom{8x^2, 8}$

Guest Jun 30, 2022

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Best Answer

We know that $ab = 6$ , meaning the pairs of $(a,b)$ are (1,6), (2,3) (3,2), (6,1)

The coefficient of x will be $b^2x + a^2x$

Now, just try out the pairs, and find the least possible value.

BuilderBoi Jun 30, 2022

BuilderBoi · Answer 1 · 2022-06-30T03:53:43

We know that $ab = 6$ , meaning the pairs of $(a,b)$ are (1,6), (2,3) (3,2), (6,1)

The coefficient of x will be $b^2x + a^2x$

Now, just try out the pairs, and find the least possible value.