Question

What is the value of a if a equals to axaxa=a+a+a

Answer 1

`\huge\boxed{a=0\ \vee\ a=-\sqrt3\ \vee\ a=\sqrt3}`

Explanation:

`a\cdot a\cdot a=a+a+a\\\\a^3=3a\qquad|\text{subtract } 3a\ \text{from both sides}\\\\a^3-3a=0\qquad|\text{distribute}\\\\a(a^2-3)=0\iff a=0\ \vee\ a^2-3=0\\\\a=0\ \vee\ a^2=3\\\\a=0\ \vee\ a=-\sqrt3\ \vee\ a=\sqrt3`