If x + \frac{1}{x} = 4 for a non-zero real number x, what is the value of x^2 + \frac{1}{x^2}?

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{"content":[{"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 1:"},{"type":"text","text":" Start with the given equation:"}],"type":"paragraph"},{"attrs":{"latex":"x + \frac{1}{x} = 4"},"type":"math_block"},{"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 2:"},{"type":"text","text":" Square both sides of the equation:"}],"type":"paragraph"},{"type":"math_block","attrs":{"latex":"\left(x + \frac{1}{x}\right)^2 = 4^2 \implies x^2 + 2(x)\left(\frac{1}{x}\right) + \frac{1}{x^2} = 16"}},{"content":[{"marks":[{"type":"bold"}],"text":"Step 3:","type":"text"},{"text":" Simplify the middle term ","type":"text"},{"attrs":{"latex":"2(x)(1/x) = 2"},"type":"math_inline"},{"text":":","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"x^2 + 2 + \frac{1}{x^2} = 16"},"type":"math_block"},{"content":[{"text":"Step 4:","type":"text","marks":[{"type":"bold"}]},{"type":"text","text":" Subtract "},{"attrs":{"latex":"2"},"type":"math_inline"},{"text":" from both sides:","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"x^2 + \frac{1}{x^2} = 16 - 2 = 14"},"type":"math_block"},{"content":[{"text":"So the value is ","type":"text"},{"attrs":{"latex":"14"},"type":"math_inline"},{"type":"text","text":"."}],"type":"paragraph"}],"type":"doc"}

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