Question : If $a^{2}+1=a$, the value of $a^{3}$ is:
Option 1: 0
Option 2: 1
Option 3: –1
Option 4: 2
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Correct Answer: –1
Solution : Given: $a^{2}+1=a$ ⇒ $a^{2}-a=-1$ ⇒ $a(a-1)=-1$ Now, $a-1=a^2$ ⇒ $a\times (a-1)=a×a^2$ ⇒ $a^3=-1$ Hence, the correct answer is –1.
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