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If x+1/x=3, calculate x^2+1/(x^2),\ x^3+...

If `x+1/x=3,` calculate `x^2+1/(x^2),\ x^3+1/(x^3)` and `x^4+1/(x^4)`

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To solve the problem where \( x + \frac{1}{x} = 3 \), we need to calculate \( x^2 + \frac{1}{x^2} \), \( x^3 + \frac{1}{x^3} \), and \( x^4 + \frac{1}{x^4} \). Let's break it down step by step. ### Step 1: Calculate \( x^2 + \frac{1}{x^2} \) 1. Start with the given equation: \[ x + \frac{1}{x} = 3 \] ...
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