Question 201440
"If {{{x+1/x=8}}}, what is the value of {{{x^4+1/x^4}}}? "
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{{{x+1/x=8}}} Multiply thru by x
{{{x^2 + 1 = 8x}}}
{{{x^2 - 8x + 1 = 0}}}
*[invoke solve_quadratic_equation 1,-8,1]
{{{x = 4+sqrt(15)}}}
{{{x^2 = 31 + 8sqrt(15)}}}
{{{x^4 = 1921 + 496sqrt(15)}}}
{{{x^4+1/x^4}}} = {{{(1922+496sqrt(15))/(1921+496sqrt(15))}}}
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{{{x = 4-sqrt(15)}}}
{{{x^2 = 1 - 8sqrt(15)}}}
{{{x^4 = 961 - 16sqrt(15)}}}
{{{x^4+1/x^4}}} = {{{(962-16sqrt(15))/(961-16sqrt(15))}}}