Can this be really solved?
Algebra
Level
5
\[\large {{ x }^{ 5 }-7{ x }^{ 4 }-1=0}\]
If \(r_{1}, r_{2}, r_{3}, r_{4}, r_{5}\) are the roots of the equation above, find the value of expression below.
\[\large{\frac { 1 }{ { r }_{ 1 }^{ 20 } } +\frac { 1 }{ { r }_{ 2 }^{ 20 } } +\frac { 1 }{ { r }_{ 3 }^{ 20 } } +\frac { 1 }{ { r }_{ 4 }^{ 20 } } +\frac { 1 }{ { r }_{ 5 }^{ 20 } } }\]
by
Lakshya Sinha