Найдите сумму квадратов корней уравнения 4x² - 7x - 1 = 0 ​

По теореме Виета :

Найдем сумму квадратов корней квадратного уравнения:

Відповідь:

1,75

Пояснення:

За теоремою Вієта сума коренів рівняння дорівнює

x₁ + x₂ = -b/a,

а добуток:  x₁x₂=c/a

а=4, b=-7, c=-1

Тому x₁ + x₂ =7/4=1,75

x₁x₂=-1/4

x₁²+x₂²=(x₁+x₂)²-2x₁x₂=(1.75)²-2*(-0.25)=3.5625

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х - 4 = 0   

х = 4

ответ: х  = 4