If \(a=3\), what is the value of \(a^2+a^{-1}\)?
Answer and explanation
Correct answer: \(\frac{28}{3}\)
Substituting \(a=3\), we get \(a^2=3^2=9\) and \(a^{-1}=\frac{1}{a}=\frac{1}{3}\). Therefore, \(a^2+a^{-1}=9+\frac{1}{3}=\frac{28}{3}\). Option A results from confusing the addition with subtraction; remember that a negative exponent denotes a reciprocal, not a negative value.
Frequently asked questions
What is the correct answer to this question?
\(\frac{28}{3}\)
Why is this the correct answer?
Substituting \(a=3\), we get \(a^2=3^2=9\) and \(a^{-1}=\frac{1}{a}=\frac{1}{3}\). Therefore, \(a^2+a^{-1}=9+\frac{1}{3}=\frac{28}{3}\). Option A results from confusing the addition with subtraction; remember that a negative exponent denotes a reciprocal, not a negative value.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Operations on real numbers and the laws of exponents.
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