If x + 1/x = 2, then the value of x^2 + 1/x^2 is:

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{"content":[{"content":[{"marks":[{"type":"bold"}],"text":"Step 1 (Square both sides):","type":"text"},{"text":" We are given ","type":"text"},{"attrs":{"latex":"x + \frac{1}{x} = 2"},"type":"math_inline"},{"text":". Squaring both sides of the equation:","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"\left(x + \frac{1}{x}\right)^2 = 2^2"},"type":"math_block"},{"attrs":{"latex":"x^2 + 2(x)\left(\frac{1}{x}\right) + \frac{1}{x^2} = 4"},"type":"math_block"},{"type":"paragraph","content":[{"marks":[{"type":"bold"}],"text":"Step 2 (Simplify the Middle Term):","type":"text"},{"text":" Since ","type":"text"},{"attrs":{"latex":"2(x)(1/x) = 2"},"type":"math_inline"},{"type":"text","text":":"}]},{"type":"math_block","attrs":{"latex":"x^2 + 2 + \frac{1}{x^2} = 4"}},{"content":[{"marks":[{"type":"bold"}],"text":"Step 3 (Isolate the Target Term):","type":"text"},{"text":" Subtract 2 from both sides:","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"x^2 + \frac{1}{x^2} = 4 - 2 = 2"},"type":"math_block"},{"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 4 (Conclusion):"},{"type":"text","text":" The value is "},{"attrs":{"latex":"2"},"type":"math_inline"},{"text":", which is option index ","type":"text"},{"text":"3","type":"text","marks":[{"type":"code"}]},{"text":" in ","type":"text"},{"marks":[{"type":"code"}],"text":"['1/4', '1', '3', '2']","type":"text"},{"type":"text","text":"."}],"type":"paragraph"}],"type":"doc"}

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