уравнение х^2+mx+6=0 имеет корни х1 и х2.Выразите(х1 -х2)^2 через m. Created by varyenjka. algebra-ru

уравнение х^2+mx+6=0 имеет корни х1 и х2.Выразите(х1 -х2)^2 через m...

m11m

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X² + mx + 6=0

По т. Виета:
x₁ * x₂ =6
x₁+x₂= -m

(x₁+x₂)² = (-m)²
x₁² + 2x₁x₂+x₂²=m²
x₁² + 2*6 + x₂² =m²
x₁² + x₂² = m² - 12

(x₁ - x₂)²=x₁² - 2x₁x₂ + x₂²=x₁² - 2*6 + x₂²=x₁² + x₂² - 12=m² - 12 - 12=
=m² - 24

Ответ: m² - 24.

1 votes Thanks 1

mikael2

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X1*x2=6 x1+x2=-m

(x1-x2)²=x1²+x2²-2x1*x2=(x1+x2)²-4x1*x2=m²-4*6=m²-24

0 votes Thanks 1

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