Evaluate an Algebraic Expression
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A positive real number $x$ satisfies $$x+\frac{1}{x}=3.$$ What is the value of $$x^4+\frac{1}{x^4}?$$ A) 31 B) 47 C) 49 D) 63 E) 79
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Step by Step Written Solution
Hi Feyza, let's solve this together. We are given that a positive real number x satisfies x plus one over x equals three, and we need to find the value of x to the power of four plus one over x to the power of four.
Problem Setup
To solve this, let's start with our given equation and square both sides.
When we expand the left side, we get x squared plus two times x times one over x, plus one over x squared, all equal to nine.
Since x times one over x is just one, this simplifies beautifully.
Now, we subtract two from both sides to find the value of x squared plus one over x squared.
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