Question

What are the excluded values of the function y= 8/x^2-25

Answer 1

Answer:

  8

——

 x2

Step-by-step explanation:

Equation at the end of step  1  :

        8    

 y -  (—— -  25)  = 0  

       x2    

Step  2  :

Rewriting the whole as an Equivalent Fraction :

2.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  x2  as the denominator :

         25     25 • x2

   25 =  ——  =  ———————

         1        x2    

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

8 - (25 • x2)     8 - 25x2

—————————————  =  ————————

     x2              x2    

Equation at the end of step  2  :

      (8 - 25x2)

 y -  ——————————  = 0  

          x2    

Step  3  :

Rewriting the whole as an Equivalent Fraction :

3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  x2  as the denominator :

         y     y • x2

    y =  —  =  ——————

         1       x2  

Trying to factor as a Difference of Squares :

3.2      Factoring:  8 - 25x2  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  8  is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Adding fractions that have a common denominator :

3.3       Adding up the two equivalent fractions

y • x2 - ((8-25x2))     yx2 + 25x2 - 8

———————————————————  =  ——————————————

        x2                    x2      

Trying to factor a multi variable polynomial :

3.4    Factoring    yx2 + 25x2 - 8  

Try to factor this multi-variable trinomial using trial and error  

Factorization fails

Equation at the end of step  3  :

 yx2 + 25x2 - 8

 ——————————————  = 0  

       x2      

Step  4  :

When a fraction equals zero :

4.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 yx2+25x2-8

 —————————— • x2 = 0 • x2

     x2    

Now, on the left hand side, the  x2  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  yx2+25x2-8  = 0

Solving a Single Variable Equation :

4.2     Solve   yx2+25x2-8  = 0

Answer 2

Answer:

I believe it's B.)5 and -5

Step-by-step explanation:

Hope this helps :))