Help me Please.

Roots: find the square roots of the following polynomials.

4x^{2}/y^{2} - 36x/y + 81

ManuelBautista2019 Feb 1, 2018

#1**+1 **

OK.....this looks a little daunting.....let's make it easier

Let x /y = "a"

So x^2 / y^2 = (x /y)^2 = "a^2"

Now.....we have someting that is a little more familiar....so....

4 (x^2/y^2) - 36 (x/y) + 81 becomes

4a^2 - 36a + 81 let us guess that the factorization of this is

(2a - 9) (2a - 9) verify for yourself that this is the correct factoring

(2a - 9)^2

But.....also ....notice that

[ -(2a - 9) ] [ - (2a - 9) ] will also produce the same result = [ - (2a - 9) ]^2

So......the square roots are

±(2a - 9) ....so....just back-substitute and we have

± [ 2(x/y) - 9 ]

CPhill Feb 1, 2018