# Can Vieta help?

Algebra Level 4

$\large { x }^{ 3 }-{ 453x }^{ 2 }+68402x-3442800$

If the expression above has 3 real roots ${ r }_{ 1 },{ r }_{ 2 },{ r }_{ 3 }$ in an arithmetic progression having common difference 1 then find the value of

${ { r }_{ 1 } }^{ 2 }+{ { r }_{ 2 } }^{ 3 }+{ { r }_{ 3 } }^{ 2 }.$

Note: The exponents in the expression are indeed $2, 3, 2$.

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