Question

Quais são as raizes da equação x² - 10x + 20 = 0

Answer 1

Utilizando Bhaskara, temos:

$\Delta~=~(-10)^2-4.1.20~=~100~-~80~=~20\\\\\\x'~=~\frac{10+\sqrt{20}}{2~.~1}~=~\frac{10+\sqrt{2^2~.~5}}{2}~=~\frac{10+2\sqrt{5}}{2}~=~\boxed{5+\sqrt{5}}\\\\\\x''~=~\frac{10-\sqrt{20}}{2~.~1}~=~\frac{10-\sqrt{2^2~.~5}}{2}~=~\frac{10-2\sqrt{5}}{2}~=~\boxed{5-\sqrt{5}}$