If-p-q-and-r-are-the-roots-of-equation-x-3-3x-2-1-0-then-find-the-value-of-3p-2-1-3-3q-2-1-3-3r-2-1-3-

Question Number 190536 by cortano12 last updated on 05/Apr/23

If p, q and r are the roots of equation

x^{3} - {3 x}^{2} + 1 = 0 then find the value

of \sqrt[3]{3 p - 2} + \sqrt[3]{3 q - 2} + \sqrt[3]{3 r - 2}

Answered by Frix last updated on 05/Apr/23

t = \sqrt[3]{3 x - 2} \Leftrightarrow x = \frac{t^{3} + 2}{3}

Inserting, transforming

t^{9} - 3 t^{6} - 24 t^{3} - 1 = 0

Searching for factors (using software) \Rightarrow

t^{3} + 0 t^{2} - 3 t - 1 [the other factor has no real roots]

\Rightarrow answer is 0

Facebook Tweet Pin