Question

x²+5x+1=0 найти: x1²+x2²

Answer 1

Ответ:

10

Объяснение:

$D=5^{2} -4*1=21$

$\sqrt{D} =\sqrt{21}$

$x_{1} =\frac{-5-\sqrt{21} }{2} =-\frac{5+\sqrt{21} }{2}$

$x_{2} =\frac{-5+\sqrt{21} }{2}$

$x^{2}_{1} +x^{2}_{2} =(-\frac{5+\sqrt{21} }{2})^2+(\frac{-5+\sqrt{21} }{2})^2=\frac{36+10\sqrt{21} }{4} +\frac{4-10\sqrt{21} }{4}=\frac{40}{4}=10$