Question 897680
a+b=3 and a^2+b^2=30
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b = 3-a
a^2 + (3-a)^2 = 30
2a^2 - 6a + 9 = 30
2a^2 - 6a - 27 = 0
*[invoke solve_quadratic_equation 2,-6,-27]
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{{{a = (3 + 3sqrt(7))/2}}}
{{{b = (3 - 3sqrt(7))/2}}}
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Someone has to cube those and add them.
You need the practice more than I do.
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{{{a = (3 + 3sqrt(7))/2 = (3/2)*(1 + sqrt(7))}}}
{{{a^3 = (3/2)^3*(1 + 3sqrt(7) + 3*7 + 7sqrt(7))}}}
{{{b^3 = (3/2)^3*(1 - 3sqrt(7) + 3*7 - 7sqrt(7))}}}
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{{{a^3+b^3= (3/2)^3*(2 + 42)}}}
= (27/8)*44
= 297/2