Are vieta's formulas required

Algebra Level 4

Let A A and B B be the roots of the polynomial x 2 − 17 x − 2 x^2-17x-2 . And let a n = A n − B n a_n = A^n - B^n . Find k = ⌊ a 10 − 2 a 8 2 a 9 ⌋ k= \left \lfloor \dfrac{a_{10} - 2a_8}{2a_9} \right \rfloor .


The answer is 8.

Samardeep Sarna by samardeep sarna , 23, India

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1 solution

Otto Bretscher
Apr 15, 2016

As we have seen in many such problems , we have a 10 − 17 a 9 − 2 a 8 = 0 a_{10}-17a_9-2a_8=0 so that k = ⌊ 17 a 9 2 a 9 ⌋ = 8 k=\left \lfloor\frac{17a_9}{2a_9}\right \rfloor=\boxed{8}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

How many times will this problem be posted ?? BTW (+1)

Rishabh Jain - 5 years, 2 months ago

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Too many times..I remember seeing it atleast two times. Nice solution, Sir :)

B.S.Bharath Sai Guhan - 5 years, 1 month ago

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