SOLUTION: Consider the equation 4x2 - 9 = 0 Let's try to solve it as follows: 4x2 - 9 = 0 (2x - 3)2 = 0 2x - 3 = 0 2x = 3 x = 3/2 Is this solution correct and if not why and what i

Algebra ->  Rational-functions -> SOLUTION: Consider the equation 4x2 - 9 = 0 Let's try to solve it as follows: 4x2 - 9 = 0 (2x - 3)2 = 0 2x - 3 = 0 2x = 3 x = 3/2 Is this solution correct and if not why and what i      Log On


   

Question 67132: Consider the equation
4x2 - 9 = 0
Let's try to solve it as follows:
4x2 - 9 = 0
(2x - 3)2 = 0
2x - 3 = 0
2x = 3
x = 3/2
Is this solution correct and if not why and what is the real solution?
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
4x^2 - 9 = 0
This form is called "difference of squares".
This is the way it factors:
a^2-b^2=(a-b)(a+b)
In your problem a=2x and b=3
So you factor the left side to get:
(2x-3)(2x+3)=0
Since the product is zero one of the factors must be zero.
So: 2x-3=0 or 2x+3=0
Then x=3/2 or x=-3/2
-------------
That is the standard way to proceed with your problem.
Cheers,
Stan H.

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
4x² - 9 = 0
Let's try to solve it as follows:
4x² - 9 = 0
(2x - 3)² = 0
2x - 3 = 0
2x = 3
x = 3/2 
Is this solution correct and if not why and what is the real solution?

No,
4x² - 9 does not factor as (2x - 3)²

  4x² - 9 = 0           4x² - 9 = 0  write as difference of squares    
(2x - 3)² = 0      (2x)² - (3)² = 0  factor difference of squares
   2x - 3 = 0  (2x - 3)(2x + 3) = 0  Set each factor = 0 & solve
       2x = 3   2x - 3 = 0;       2x + 3 = 0                 
        x = 3/2     2x = 3;           2x = -3
                     x = 3/2;          x = -3/2

Correct solutions:  3/2 and -3/2

Edwin