MathDB
nice problem

Source: Netherlands 1991

June 28, 2009
algebrapolynomialalgebra proposed

Problem Statement

Three real numbers a,b,c a,b,c satisfy the equations a\plus{}b\plus{}c\equal{}3, a^2\plus{}b^2\plus{}c^2\equal{}9, a^3\plus{}b^3\plus{}c^3\equal{}24. Find a^4\plus{}b^4\plus{}c^4.