Question

sendo x2+1/x2=5, calcule o valor de (x+2/x)2

Answer 1

$( \frac{x+2}{x} )^2 = \frac{x^2+4x+4}{x^2} =1+ \frac{4}{x} + \frac{4}{x^2} \\ \\ \frac{x^2+1}{x^2} = 5 \\ 1+ \frac{1}{x^2} =5 \\ \frac{1}{x^2} =4 \\ \frac{1}{x} =2 \\ \\ Substituindo: \\ \\ ( \frac{x+2}{x} )^2 =1+4*2+4*4 = 1+8+16=25$