Chapter 4.7, Problem 37E

To determine

To solve: $\sqrt{x-5}=\sqrt[3]{x-3}$

Answer to Problem 37E

  $x\simeq 7.88$

Explanation of Solution

Given information: $\sqrt{x-5}=\sqrt[3]{x-3}$

Calculation:

Given:

  $\sqrt{x-5}=\sqrt[3]{x-3}$

Square both sides. The square can go outside or inside.

  $\begin{array}{l}x-5=\sqrt[3]{{\left(x-3\right)}^2}\\ x-5=\sqrt[3]{x^2-6x+9}\end{array}$

Cube both sides

  ${\left(x-5\right)}^3=x^2-6x+9$

Expand

  $x^3-15x^2+75x-125=x^2-6x+9$

Collect terms

  $x^3-16x^2+81x-134=0$

  

Graph to see solution is $x\simeq 7.88$