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Question
If \[x + \frac{1}{x}\] 4, then \[x^4 + \frac{1}{x^4} =\]
Options
196
194
192
190
Solution
In the given problem, we have to find the value of `x^4 + 1/x^4`
Given `x+ 1/x = 4`
We shall use the identity `(a+b)^2 = a^2 +b^2 + 2ab`
Here put,`x+ 1/x = 4`
`(x+ 1/x)^2 = x^2 + 1/x^2 + 2 (x xx 1/x)`
`(4)^2 = x^2 + 1/x^2 + 2 (x xx 1/x )`
`16 = x^2 + 1/x^2 + 2`
` 16 -2 = x^2 + 1/x^2`
`14 = x^2 + 1/x^2`
Squaring on both sides we get,
`(14)^2 = (x^2 + 1/x^2 )^2`
`14 xx 14 = (x^2)^2 + (1/x^2) ^2 + 2 xx x^2 xx 1/x^2`
`196 = x^4 + 1/x^4 + 2`
`196 -2 = x^4 + 1/x^4`
`194= x^4 + 1/x^4`
Hence the value of `x^4 + 1/x^4`is 194.
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