Question

if x+ 1/x=5find value of x² + 1/x²

Answer 1

x+1/x=5
squaring both sides
x2 +1/x2+ 2x/x=25
x2+1/x2+2= 25
x2+1/x2= 25-2=23

Answer 2

if $x + \frac{1}{x} = 5$
and
 [tex][ x+ \frac{1}{x} ]^{2} = x^{2} + \frac{1}{ x^{2} } + 2( x* \frac{1}{x} ) \\= x^{2} + \frac{1}{ x^{2} } + 2 [/tex]

∴$x^{2} + \frac{1}{ x^{2} } = [ x+ \frac{1}{ x}]^{2} - 2$

Now, we put the equation this way 
$x^{2} + \frac{1}{ x^{2} } = [ x+ \frac{1}{x}]^{2} - 2 \\ x^{2} + \frac{1}{ x^{2} } = 5 ^{2} - 2 \\ x^{2} + \frac{1}{ x^{2} } = 25-2 \\ x^{2} + \frac{1}{ x^{2} } = 23$