Advanced MathVery hardProduct of conjugate expressions with reciprocals
Advanced Math practice question
For x ≠ 0, which of the following is equivalent to (x + 1/x)(x − 1/x)?
- A. x² − 1/x²Correct
- B. x² − 1
- C. x² + 1/x²
- D. x² − 2 + 1/x²
Answer: A. x² − 1/x²
(p + q)(p − q) = p² − q² with p = x and q = 1/x.
Why the other answers are wrong
- B. x² − 1
- The square of 1/x is 1/x², not 1.
- C. x² + 1/x²
- The sign of the second term is negative.
- D. x² − 2 + 1/x²
- That is (x − 1/x)², a square, not a product of conjugates.
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