Question

If x + 1/x = 5, then evaluate x^6 + 1/x^6

Answer 1

 For finding the value of $x^{6}+ \frac{1}{x^6}$
we can take
$x+ \frac{1}{x}=5$
[tex](x+ \frac{1}{x})^3=(5)^3 [/tex]
$x^3+ \frac{1}{x^3}+3*x* \frac{1}{x}(x+ \frac{1}{x})=125$
$x^3+ \frac{1}{x^3}+3*5=125$
$x^3+ \frac{1}{x^3} =125-15$
$x^3+ \frac{1}{x^3} =110$
Therefore
$(x^3+ \frac{1}{x^3})^2=(110)^2$
$(x^3)^2+2*x^3* \frac{1}{x^3}+( \frac{1}{x^3})^2= 12100$
$x^6+ \frac{1}{x^6}=12100-2$
$x^6+ \frac{1}{x^6} =12098$