Chapter 10.1, Problem 56E

To determine

To find the solution.

Answer to Problem 56E

  $\left(x,y\right)=\left(2,1\right),\left(5,4\right)$

Explanation of Solution

Given information: $x-1=\sqrt{5x-9}$

Formula Used: Factorization and ${\left(a-b\right)}^2=a^2-2ab+b^2$

Calculation:

  $x-1=\sqrt{5x-9}$

Now, squaring both sides.

  ${\left(x-1\right)}^2={\left(\sqrt{5x-9}\right)}^2$

Now, Use formula ${\left(a-b\right)}^2=a^2-2ab+b^2$

  $x^2-2x+1=5x-9$

So, equate

  $x^2-2x-5x+1+9=0$

Now,

  $x^2-7x+10=0$

So,

  $x^2-2x-5x+10=0$

Now,

  $x\left(x-2\right)-5\left(x-2\right)=0$

So,

  $\left(x-2\right)\left(x-5\right)=0$

Hence,

  $x=2$ or $x=5$

Now, find y

  $y=x-1$ or $y\text{'}=\sqrt{5x-9}$

Put value of x

  $y=2-1$ or $y\text{'}=\sqrt{\left(5\times 5\right)-9}$

So,

  $y=1$ or $y\text{'}=\sqrt{16}$

Hence,

  $y=1$ or $y\text{'}=4$

So,

Collide at $\left(x,y\right)=\left(2,1\right),\left(5,4\right)$

Now, graphical utility$y=x-1$ and $y\text{'}=\sqrt{5x-9}$

• Graph of $y=x-1$

  $\begin{array}{cccc}x& 2& 3& 4\\ y& 1& 2& 3\end{array}$

• Graph of $y\text{'}=\sqrt{5x-9}$

  $\begin{array}{cccc}x& 2& 3& 4\\ y\text{'}& 1& 2.45& 3.32\end{array}$