4 years ago

Replace ∗ with a monomial so that the trinomial may be represented by a square of a binomial: 25a^2+ ∗ + 1/4b^2

1 answer:

7 0

The square of a binomial is a pattern you would do well to remember.
.. (x +y)^2 = x^2 +2xy +y^2

Your expression has x^2 = 25a^2, so x = 5a. It also has y^2 = (b^2)/4, so y = b/2.
then the middle term is
.. 2xy = 2(5a)(b/2) = 5ab

The trinomial is
.. 25a^2 +5ab +(1/4)b^2 = (5a +b/2)^2

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4 years ago

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You have the following inequality given in the problem shown above:

(x^2-1)/(x^2+5x+4)≤0

1. To solve it, you must factor it and then you must make the study of the signs.

2. Once you do the proccedure mentioned above, you obtain the following solutions:

-4<x<-1

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3. You can graph the inaquality given in the problem, as you can see in the figure attached.