Question

Daca x+ 1/x = 5 Atunci x la a patra + 1/x la a patra = ?Dau coroanaaaa

Answer 1

$x+ \frac{1}{x}=5$, ridicam egalitatea la patrat, obtinem : 
$x^{2} +2*x* \frac{1}{x}+ \frac{1}{ x^{2} }=25,adica,x^{2} +2+ \frac{1}{ x^{2} } =25,sau, x^{2} +\frac{1}{ x^{2} }=23,$ ridicand din nou la patrat, se obtine: $x^{4} +2 x^{2} * \frac{1}{ x^{2} } + \frac{1}{ x^{4} } =529,sau, x^{4} +2+ \frac{1}{ x^{4} } =527,deci: x^{4} + \frac{1}{ x^{4} }=525$