Question 132974
{{{x = sqrt(6/7)}}}
{{{(x + 1/x)^2 = x^2 + 2 + (1/x)^2}}}
{{{ x^2 + 2 + (1/x)^2 = (sqrt(6)/sqrt(7))^2 + 2 + (sqrt(7)/sqrt(6))^2}}}
{{{(sqrt(6)/sqrt(7))^2 + 2 + (sqrt(7)/sqrt(6))^2 = 6/7 + 2 + 7/6}}}
{{{6/7 + 2 + 7/6 = (36 + 84 + 49)/42}}}
{{{169/42}}} answer
check:
{{{x = sqrt(6)/sqrt(7)}}}
{{{x = .9258}}}
{{{(x + 1/x)^2 = (.9258 + 1.080)^2}}}
{{{(.9258 + 1.080)^2 = 4.0237}}}
{{{169/42 = 4.0238}}}
close enough