Is it as hard as it looks?

Algebra Level 5

a+b+c=6a2+b2+c2=78a3+b3+c3=420a5+b5+c5=xa+b+c=6\\ { a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 }=78\\ { a }^{ 3 }+{ b }^{ 3 }+{ c }^{ 3 }=420\\ { a }^{ 5 }+{ b }^{ 5 }+{ c }^{ 5 }= x

Find xmod50 {x} \mod{50} .

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