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Problem 7 - Entrance Test

If x + 1/x = 5, find the value of x^2 + 1/x^2.

Correct: A

Given x + 1/x = 5. Square both sides: (x + 1/x)^2 = 5^2 Using (a+b)^2 = a^2 + 2ab + b^2, with a = x and b = 1/x. x^2 + 2(x)(1/x) + (1/x)^2 = 25 x^2 + 2 + 1/x^2 = 25 x^2 + 1/x^2 = 25 - 2 x^2 + 1/x^2 = 23.