Question

if x+1/x=5 find the value of x4+/x²

Answer 1

Hey There!

Did you mean : x² + 1/x²

Or : x⁴ + 1/x⁴
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Given:

$x + \frac{1}{x} = 5 \\ \\ \bold{on \: squaring \: both \: sides} \\ \\ (x + \frac{1}{x} ) {}^{2} = (5) {}^{2} \\ \\ x {}^{2} + \frac{1}{x {}^{2}} + 2 \times \cancel x \times \frac{1}{ \cancel x} = 25 \\ \\ x {}^{2} + \frac{1}{x {}^{2} } + 2 = 25 \\ \\ x {}^{2} + \frac{1}{x {}^{2} } = 25 - 5 \\ \\ \bold{ \boxed {\bold{x {}^{2} + \frac{1}{x {}^{2} } = 23}}}$

Now, Again

$\bold{on \: squaring \: both \: sides} \\ \\ (x {}^{2} + \frac{1}{x {}^{2} } ) {}^{2} = (23) {}^{2} \\ \\ x {}^{4} + \frac{1}{x {}^{4}} + 2 \times \cancel{ x {}^{2}} \times \frac{1}{ \cancel{x {}^{2} }} = 529 \\ \\ x {}^{4} + \frac{1}{x {}^{4}} + 2 = 529 \\ \\ x {}^{4} + \frac{1}{x {}^{4}} = 529 - 2 \\ \\ \boxed{ \bold{ x {}^{4} + \frac{1}{x {}^{4}} = 527}}$

Thanks for the question!