Question

if x^4+1/x^4=2 find the value of x^2+1/x^2

Answer 1

Step-by-step explanation:

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Given that,

\begin{lgathered}x - \frac{1}{x} = 2 \\ \\ Squaring \: both \: sides \: \\ we \: get ,\\ \\(x - \frac{1}{x}) {}^{2} = 2 {}^{2} \\ \\ {x}^{2} + \frac{1}{x {}^{2} } - 2 \times x \times \frac{1}{x} = 4 \\ \\ {x}^{2} + \frac{1}{x {}^{2} } - 2 = 4 \\ \\ {x}^{2} + \frac{1}{x {}^{2} } = 6\\ \\ Again, \: squaring \: both \: sides \\ we \: get ,\\ \\ {x}^{4} + \frac{1}{ {x}^{4} } + 2 \times x {}^{2} \times \frac{1}{x {}^{2} } = {6}^{2} \\ \\ {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 36 \\ \\ {x}^{4} + \frac{1}{ {x}^{4} } = 34\end{lgathered}x−x1=2Squaringbothsidesweget,(x−x1)2=22x2+x21−2×x×x1=4x2+x21−2=4x2+x21=6Again,squaringbothsidesweget,x4+x41+2×x2×x21=62x4+x41+2=36x4+x41=34

Answer 2

Answer:

See this.

Step-by-step explanation:

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