If, x 9 + x 8 + x 5 + 7 x 2 − 2 x = 7
Let α , β , γ be the real roots of this equation,where α < β < γ
Let there be a triangle with sides as ∣ α ∣ , ∣ β ∣ , ∣ γ ∣
Find the Least Common Multiple of all 3 interior angles when rounded off to the nearest degree.
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Perfect but how did you get the roots?
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By graphing x 9 + x 8 + x 5 + 7 x 2 − 2 x − 7 = 0 and noting down the three intersection with x-axis. To get accurate values, I went on narrowing range of x around each intersection. As we come to more accuracy, range of y in the window was made - 0.000001 to 0.000001. I use TI-83 Plus. You may use any graphing calculator. Any more questions ? You are welcome . Google too has many graphing calculator. O R If you have zoom box, use it up to desired accuracy.
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Can you post this explanation in your answer by editing. It will explain others how to derive this answer.This will be the perfect answer to my Problem.
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@Vraj Mistry – Thanks. I have included in my solution .
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G r a p h i n g i n T I − 8 3 P l u s , ( α , β , γ ) = ( − 1 . 3 5 3 7 8 , − 0 . 9 0 6 8 8 2 5 , 0 . 9 6 8 3 3 3 6 2 ) U s i n g C o s R u l e , w e g e t a n g l e s a s 4 2 , 4 6 , 9 2 . L C M = 4 2 ∗ 4 6 = 1 9 3 2 B y g r a p h i n g x 9 + x 8 + x 5 + 7 x 2 − 2 x − 7 = 0 and noting down the three intersection with x-axis. To get accurate values, I went on narrowing range of x around each intersection. As we come to more accuracy, range of y in the window was made - 0.000001 to 0.000001. I use TI-83 Plus. You may use any graphing calculator. Any more questions ? You are welcome . Google too has many graphing calculator. O R Use zoom Box a few times up to required accuracy.