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jmc

algebra intermediate

Problem

If

x + \frac{1}{x} = 6

, then what is the value of

x^{2} + \frac{1}{x ^{2}}

?

Solution

Squaring the equation provided, we get

x^{2} + 2 (x) (\frac{1}{x}) + \frac{1}{x ^{2}} = 36,

so

x^{2} + \frac{1}{x ^{2}} = 34 .

Final answer

34