If x^2 - 2x + 1 = 0, then x^2 + 1/x^2 is ________.

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{"type":"doc","content":[{"content":[{"marks":[{"type":"bold"}],"text":"Step 1 (Solve for x):","type":"text"},{"text":" We are given the quadratic equation:","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"x^2 - 2x + 1 = 0"},"type":"math_block"},{"content":[{"text":"This is a perfect square trinomial:","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"(x - 1)^2 = 0 \implies x - 1 = 0 \implies x = 1"},"type":"math_block"},{"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 2 (Substitute x into Target expression):"},{"type":"text","text":" We want to find the value of "},{"attrs":{"latex":"x^2 + \frac{1}{x^2}"},"type":"math_inline"},{"text":". Substituting ","type":"text"},{"attrs":{"latex":"x = 1"},"type":"math_inline"},{"text":":","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"1^2 + \frac{1}{1^2} = 1 + 1 = 2"},"type":"math_block"},{"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 3 (Conclusion):"},{"text":" The value of the expression is exactly ","type":"text"},{"marks":[{"type":"code"}],"text":"2","type":"text"},{"text":".","type":"text"}],"type":"paragraph"}]}

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