f-x-x-3-16x-2-57x-1-f-a-0-f-b-0-f-c-0-a-1-5-b-1-5-c-1-5-

Question Number 204595 by SEKRET last updated on 22/Feb/24

f (x) = x^{3} - 16 x^{2} - 57 x + 1

f (a) = 0 f (b) = 0 f (c) = 0

\sqrt[5]{a} + \sqrt[5]{b} + \sqrt[5]{c} = ?

Answered by mr W last updated on 22/Feb/24

t = \sqrt[5]{x} \Rightarrow x = t^{5}

t^{15} - 16 t^{10} - 57 t^{5} + 1 = 0

(t^{3} - t^{2} - 2 t + 1) (t^{12} + t^{11} + \dots + 2 t + 1) = 0

t^{3} - t^{2} - 2 t + 1 = 0

\Rightarrow \sqrt[5]{a} + \sqrt[5]{b} + \sqrt[5]{c} = t_{1} + t_{2} + t_{3} = 1 ✓

Commented by SEKRET last updated on 22/Feb/24

thank you sir

Commented by Satyam1234 last updated on 23/Feb/24

H o w t o g e t t h i r d s t e p f r o m s e c o n d ?

Commented by mr W last updated on 23/Feb/24

f a c t o r i z a t i o n o f p o l y n o m i a l w i t h

h e l p o f c o m p u t e r p r o g r a m

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