Question

x+1/x=3 calculati x∧2 + 1/x∧2

Answer 1

Aplici formula :
$(a+b)^{2} = a^{2} + b^{2} +2*a*b$
unde a=x si b=1/x si obtii:
$(x+ \frac{1}{x} )^{2} = x^{2} + ( \frac{1}{x} )^{2} +2*x* \frac{1}{x} =$
=$x^{2} + \frac{1}{ x^{2} } +2$
Deci:
$3^{2} =(x^{2} + \frac{1}{ x^{2} })+2$
$9 =(x^{2} + \frac{1}{ x^{2} })+2$
$x^{2} + \frac{1}{ x^{2} } =9-2=7$