Question : If $a+\frac{1}{a}=1$, then the value of $\frac{a^2-a+1}{a^2+a+1}$ is $(a\neq 0)$:
Option 1: 1
Option 2: –1
Option 3: 0
Option 4: 2
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Answer (1)
19th Jan, 2024
Correct Answer: 0
Solution :
Given: $a+\frac{1}{a}=1$
⇒ $\frac{a^2+1}{a}=1$
⇒ $a^2+1=a$
⇒ $a^2-a+1=0$
Now, $\frac{a^2–a+1}{a^2+a+1}=\frac{0}{a^2+a+1}=0$
Hence, the correct answer is 0.
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