Question 1182754
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{{{x^2 = x+3}}}
{{{x^2-x-3 = 0}}}
{{{x = (1+sqrt(13))/2}}} or {{{x = (1-sqrt(13))/2}}}<br>
(1)
{{{x = (1+sqrt(13))/2}}}
{{{x^2 = (14+2sqrt(13))/4 = (7+sqrt(13))/2}}}
{{{x^3 = ((7+sqrt(13))/2)*((1+sqrt(13))/2) = (20+8sqrt(13))/4 = 5+2sqrt(13)}}}<br>
(2)
{{{x = (1-sqrt(13))/2}}}
{{{x^2 = (14-2sqrt(13))/4 = (7-sqrt(13))/2}}}
{{{x^3 = ((7-sqrt(13))/2)*((1-sqrt(13))/2) = (20-8sqrt(13))/4 = 5-2sqrt(13)}}}<br>
ANSWER: x^3 has either of two values: {{{5+2sqrt(13)}}} or {{{5-2sqrt(13)}}}<br>