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Question
If `x^4 + 1/x^4 = 194, "find" x^2 + 1/x^2`
Sum
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Solution
Given: `x^4 + 1/x^4 = 194`
We know that,
`(x^2 + 1/x^2)^2 = x^4 + 1/x^4 + 2` ...[Using (a + b)2 = a2 + b2 + 2ab]
Now, substituting the given value:
`(x^2 + 1/x^2)^2 = 194 + 2`
`(x^2 + 1/x^2)^2 = 196`
`x^2 + 1/x^2 = +-sqrt196`
∴ `x^2 + 1/x^2 = +-14`
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Chapter 4: Algebraic Identities - Exercise 4.3 [Page 20]
