Question

x³+1/x³ find value x+1/x=√5​

Answer 1

Answer:

$x {}^{} + \frac{1}{x {}^{} } = \sqrt{5}$

using identity

(a+b)³ = a³ + b³ + 3ab(a+b)

$(x + \frac{1}{x} ) {}^{3} = x {}^{3} + \frac{1}{x {}^{3} } + 3 \times x \times \frac{1}{x} (x + \frac{1}{x} )$

$( \sqrt{5} ) {}^{3} = x {}^{3} + \frac{1}{x {}^{3} } + 3( \sqrt{5} )$

$5\sqrt{5} - 3 \sqrt{5} = x {}^{3} + \frac{1}{x {}^{3} }$

$x {}^{3} + \frac{1}{x {}^{3} } = 2 \sqrt{5}$