Question

Найдите увеличенную в 4 раза сумму квадратов корней уравнения
x² - 3x − 8 = 0
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Answer 1

$\displaystyle\bf\\x^{2} -3x-8=0\\\\Teorema \ Vieta \ :\\\\x_{1} + x_{2} =3\\\\x_{1} \cdot x_{2} =-8\\\\\\x_{1} ^{2} +x_{2} ^{2} =(x_{1} + x_{2} )^{2} -2x_{1} x_{2} =3-2\cdot(-8)=3+16=19\\\\\\(x_{1} ^{2} +x_{2} ^{2})\cdot 4 =19\cdot 4=76$