The ratio of the interior angles of a triangle is 2 : 6 : 7. What are the angle measures? Write the angle measures from least to greatest.

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Ответ:

goblebrandon

26.03.2021

Mathematics

Using the factor theorem, we have

7x^2+x-5=7(x-a)(x-b)

and expanding gives us

$7x^2+x-5=7(x^2-(a+b)x+ab)\implies\begin{cases}ab=-5\\a+b=-1\end{cases}$

So we have

$(a-4)(b-4)=ab-4(a+b)+16=-5-4(-1)+16=\boxed{15}$

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