Suppose a,b,c satisfy the following equation: a+b+c=3; a2+ b2 +c2= 5; a3+b3+c3=7; what is a4+b4+c4 SEND ME DE ENTIRE SOLUTION

Follow Math Help Forum on Facebook and Google+

Originally Posted by kamaksh_ice Suppose a,b,c satisfy the following equation: a+b+c=3; a2+ b2 +c2= 5; a3+b3+c3=7; what is a4+b4+c4 SEND ME DE ENTIRE SOLUTION Hello, I assume that you mean aČ when you write a2. I can't give you the complete solution, only some considerations. But maybe you can use them for a start: = According to the problem this term can be reduced to: And now I need a small spark of inspiration.

Square, ...(1) Square, Thus, Square, Thus, Thus, ...(2) Use the identity, Thus, Thus, ...(3) Thus by (2) and (3) we have, Thus by (1) we have, Thus,

Originally Posted by kamaksh_ice Suppose a,b,c satisfy the following equation: a+b+c=3; a2+ b2 +c2= 5; a3+b3+c3=7; what is a4+b4+c4 You may, of course, solve the system by substitution. Unfortunately when I do this I can't get an exact answer for a without using Cardano's method. -Dan