Exercise 51 Page 62

We want to solve the given equation by factoring. Let's consider our equation. 4y^2-9/16=0 Notice that this equation follows a special pattern. It can be factored as a difference of squares. Let's factor the equation!

4y^2-9/16=0

WritePow

Write as a power

2^2y^2-(3/4)^2=0

ProdPowII

a^m b^m = (a b)^m

(2y)^2-(3/4)^2=0

FacDiffSquares

a^2-b^2=(a+b)(a-b)

(2y+3/4)(2y-3/4)=0

Now we are ready to use the Zero Product Property.

(2y+3/4)(2y-3/4)=0

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Solve using the Zero Product Property

ZeroProdProp

Use the Zero Product Property

lc2y+ 34=0 & (I) 2y- 34=0 & (II)

SubEqn

(I): LHS-3/4=RHS-3/4

l2y=- 34 2y- 34=0

AddEqn

(II): LHS+3/4=RHS+3/4

l2y=- 34 2y= 34

(I), (II): LHS * 1/2=RHS* 1/2

ly=- 34( 12) y= 34( 12)

(I), (II): Multiply fractions

ly=- 38 y= 38

We found that the solutions to the given equation are y=- 38 and y= 38. To check our answer, we will graph the related function, f(y)=4y^2- 916, using a calculator. Note that the calculator will use the variable x instead of y. Also, as 916=0.5625, we will use the decimal instead of the fraction.

We can see that the x-intercepts are - 38, or - 0.375, and 38 or 0.375. Therefore, our solutions are correct.