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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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