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Algebra Level 4

x3453x2+68402x3442800\large { x }^{ 3 }-{ 453x }^{ 2 }+68402x-3442800

If the expression above has 3 real roots r1,r2,r3{ r }_{ 1 },{ r }_{ 2 },{ r }_{ 3 } in an arithmetic progression having common difference 1 then find the value of

r12+r23+r32.{ { r }_{ 1 } }^{ 2 }+{ { r }_{ 2 } }^{ 3 }+{ { r }_{ 3 } }^{ 2 }.

Note: The exponents in the expression are indeed 2,3,22, 3, 2 .

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