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Question
If `x - 1/x = 7` then find the value of `x^2 + 1/x^2`.
Sum
Solution
Given, `x - 1/x = 7`
Since, `(x - 1/x)^2 = x^2 + 1/x^2 - 2 * x * 1/x` ...[Using the identity, (a – b)2 = a2 + b2 – 2ab]
∴ `7^2 = x^2 + 1/x^2 - 2`
⇒ `x^2 + 1/x^2 = 49 + 2`
⇒ `x^2 + 1/x^2 = 51`
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