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Question
If `(x^2 - 1)/x = 7, "find" x^2 + 1/x^2`
Sum
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Solution
Given: `(x^2 - 1)/x = 7,`
Multiply the equation by x,
x2 − 1 = 7x
∴ x2 − 7x − 1 = 0
Dividing the equation by x,
`x^2/x - (7x)/x - 1/x = 0/x`
`x - 7 - 1/x = 0`
∴ `x - 1/x = 7`
Using the identity,
`(x - 1/x)^2 = x^2 + 1/x^2 - 2`
`(7)^2 = x^2 + 1/x^2 - 2`
`49 = x^2 + 1/x^2 - 2`
`49 + 2 = x^2 + 1/x^2`
∴ `51 = x^2 + 1/x^2`
Hence, `x^2 + 1/x^2 = 51`
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