Question

if x3 + 1/x3 = 110 then find the value of x + 1/x

Answer 1

hi friend!
Here is your Answer
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${x}^{3} + \frac{1}{ {x}^{3} } = 110 \\ \\ now \\ \\ (x + \frac{1}{x} ) {}^{3} = {x}^{3} + \frac{1 {}^{} }{ {x}^{3} } + 3(x + \frac{1}{x} ) \\ let \: a \: = \: x + \frac{1}{x} \\ \\ nw \\ \\ {a}^{3} = 110 + 3a \\ {a}^{3} - 3a - 110 = 0 \\ \\ putting \: a = 5 \\ 125 - 15 - 110 = 0 \\ 0 = 0 \\ thus \:( a \: - 5) \: is \: factor \\ \\ {a}^{2} (a \: - 5) \: + 5a (a - 5) \: + 22(a - 5) \\ \\ \: (a - 5) = 0 \: \: \\ ( {a}^{2} + 5a + 22) = 0 \\ \\ a - 5 = > x + \frac{1}{x} = 5 \: ans \\ \\ hope \: its \: helpful$

Answer 2

Answer: The answer is 5