Advanced MathVery hardSum of squares from a sum of reciprocals
Advanced Math practice question
If x + 1/x = 5, what is the value of x² + 1/x²?
Answer: 23
Square both sides: (x + 1/x)² = x² + 2 + 1/x² = 25. So x² + 1/x² = 25 − 2 = 23.
Common wrong answers
- If you answered 10
- 10 is 5 × 2, doubling instead of squaring.
- If you answered 25
- 25 is (x + 1/x)², which includes the cross term 2·x·(1/x) = 2.
- If you answered 27
- 27 adds the 2 instead of subtracting it.
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