If x - 1x = 5, what is the value of x^2 + 1x^2?

SAT Equivalent expressions Practice Question 19 (Hard)

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If $x - \frac{1}{x} = 5$ , what is the value of $x^2 + \frac{1}{x^2}$ ?

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Answer: 27

Square both sides: $\left(x - \frac{1}{x}\right)^2 = x^2 - 2 + \frac{1}{x^2} = 25$ . Add 2 to both sides: $x^2 + \frac{1}{x^2} = 27$ .

Squaring each term separately and ignoring the middle term gives 25.

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