Chapter 4, Problem 11AR

To determine

To solve the given equation, $y^2-6y+9=0$ by factoring or quadratic formula.

Answer to Problem 11AR

  $y=3$

Explanation of Solution

Given:

The equation is, $y^2-6y+9=0$

Calculation:

We can solve the given equation by using quadratic formula.

That is,

  $y=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

The given equation $y^2-6y+9=0$ is in the form of $a{y}^2+by+c=0$ . Where, $a=1,b=-6\text{ and c = 9}$ .

Now, Substitute the values in the formula then we get that,

  $\begin{array}{l}y=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ y=\frac{-\left(-6\right)\pm \sqrt{{\left(-6\right)}^2-4\left(1\right)\left(9\right)}}{2\left(1\right)}\\ y=\frac{6\pm \sqrt{36-36}}{2}\\ y=\frac{6\pm 0}{2}\\ y=3\end{array}$

Therefore, the root for the given equation, $y^2-6y+9=0$ is, $y=3$ .