Showing posts with label isolate all terms to the left. Show all posts
Showing posts with label isolate all terms to the left. Show all posts

Tuesday, August 4, 2015

IMO Solving Equation Problem: Solve the equation $x+a^3=\sqrt[3]{a-x}$ where a is real (First Solution)

Solve the equation $x+a^3=\sqrt[3]{a-x}$ where $a$ is real.

If one wants to do things in haste and quickly solve the above equation for $x$ without thinking much, one would definitely raise both sides of the equation to the third power to get rid of the cube root:

$x+a^3=\sqrt[3]{a-x}$

$(x+a^3)^3=(\sqrt[3]{a-x})^3$