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Question
If `x + 1/x = 9`, then the value of `x^2 + 1/x^2` is ______.
Options
77
79
83
85
MCQ
Fill in the Blanks
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Solution
If `x + 1/x = 9`, then the value of `x^2 + 1/x^2` is 79.
Explanation:
If `x + 1/x = 9`, we need to find the value of `x^2 + 1/x^2`.
Step 1: Square both sides of the equation:
`(x + 1/x)^2 = 9^2`
`x^2 + 2 + 1/x^2 = 81`
Step 2: Subtract 2 from both sides:
`x^2 + 1/x^2 = 81 - 2`
`x^2 + 1/x^2 = 79`
Therefore, the value of `x^2 + 1/x^2` is 79.
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