Question

if x+1/x=5 then x^5+1/x^5=?
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Answer 1

x×5+1/x×5===6x/5x

^ The left place is of multiple

Answer 2

★some important thought:-

$\implies \: (x {}^{2} + \frac{1}{x {}^{2} } )(x {}^{3} + \frac{1}{x {}^{3} } ) = x {}^{5} + \frac{1}{x {}^{5} } + x + \frac{1}{x} - - (1)$

$\implies \: x + \frac{1}{x {}^{} } = 5 \\ \\ \implies \: x {}^{2} + \frac{1}{x {}^{2} } = 5 {}^{2} - 2 \\ \\ \implies \: x {}^{2} + \frac{1}{x {}^{2} } = 23 - - (2)$

$\implies \: x {}^{3} + \frac{1}{x {}^{3} } = 5 {}^{3} - 3(5) \\ \\ \implies \: x {}^{3} + \frac{1}{ {x}^{3} } = 110 - - (3)$

we find answer eq 1 , 2 and 3

$\implies \: 23 \times 110 = x {}^{5} + \frac{1}{x {}^{5} } + 5 \\ \\ \implies \: x {}^{5} + \frac{1}{x {}^{5} } = 2530 - 5 = 2525$

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thanks