Solve the equation $x+a^3=\sqrt[3]{a-x}$ where a is real parameter.
My solution:
By observation, note that $x=a-a^3$ is a real solution for the equation $x+a^3=\sqrt[3]{a-x}$.
Showing posts with label a is real parameter. Show all posts
Showing posts with label a is real parameter. Show all posts
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:
$x+a^3=\sqrt[3]{a-x}$
$(x+a^3)^3=(\sqrt[3]{a-x})^3$
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:
$x+a^3=\sqrt[3]{a-x}$
$(x+a^3)^3=(\sqrt[3]{a-x})^3$
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