I was asked,
Use to substitution $y=a^x$ or otherwise to solve the equation $a^{3x} - 2a^{2x} + a^x = 0$.
I attained the expression,
$y^3 - y^2 + y = 0$ unable to solve further provided the given solution is $x = 0$.
I was asked,
Use to substitution $y=a^x$ or otherwise to solve the equation $a^{3x} - 2a^{2x} + a^x = 0$.
I attained the expression,
$y^3 - y^2 + y = 0$ unable to solve further provided the given solution is $x = 0$.
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Hint: $$y^3-2y^2+y=y\,(y^2-2y+1)=y\,(y-1)^2$$