Question

$ifx + \frac{1}{x} = 5 find x3 + \frac{1}{x3}$
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Answer 1

Answer:

I think Answer is 2525 .

Step-by-step explanation:

$x + \frac{1}{x} = 5 \\ (x + \frac{1}{x} ) ^{2} = {5}^{2} \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2.x. \frac{1}{x} = 25 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 25 - 2 = 23 \\ \\ x + \frac{1}{x} = 5 \\ {(x + \frac{1}{x}) }^{3} = {5}^{3} \\ {x}^{3} + \frac{1}{ {x}^{3} } + 3.x. \frac{1}{x} (x + \frac{1}{x} ) = 125 \\ {x}^{3} + \frac{1}{ {x}^{3} } + 3(5) = 125 \\ {x}^{3} + \frac{1}{ {x}^{3} } + 15 = 125 \\ {x}^{3} + \frac{1}{ {x}^{3} } = 110$

$( {x}^{2} + \frac{1}{ {x}^{2} } )( {x}^{3} + \frac{1}{ {x}^{3} } ) = 110 \times 23 \\ {x}^{5} + \frac{1}{ {x}^{5} } + x + \frac{1}{x} = 2530 \\ {x}^{5} + \frac{1}{ {x}^{5} } + 5 = 2530 \\ {x}^{5} + \frac{1}{ {x}^{5} } = 2525$

Answer 2

THE ANSWER HAD BEEN SOLVED BEFORE ME