If the system of equations x + y + z = 3 , x^3 + y^3 + z^3 = 15 and x^4 + y^4 + z^4 = 35 , has real solution x,y,z for which x^2 + y^2 + z^2 < 10 then find the value of x^5 + y^5 + z^5???
A nice algebra question with its details below?
- Posted:
- 3+ months ago by Iitaspirant
- Topics:
- detail, system, real, solution, below, question, mathematics, equations, algebra
Details:
Answers (1)
You have two lines. Where they cross, the values of x and y satisfy both equations simultaneously, so it is called a simultaneous system. There are two ways to find that point. Substitution is when you solve one equation for one variable and substitute that into the other equation.
Elimination is when you add the equations in a way to eliminate one variable. Otherwise the process is the same.
Use this process to reduce a system of three unknowns to a system of two uinkowns. Then do it again to find one answer. Do it two more times to find the other two answers.
No, this is a mess and I don't care to fiddle with it. There is nothing to be learned from it. Math is only valid when it describes reality, and I don't think this system describes anything real.
Even Wolframalpha won't do it: www.wolframalpha.com/input/?i=plot+x%2By%2Bz%3D3,+x%5E3+%2B+y%5E3+%2B+z%5E3+%3D+15,+x%5E4+%2B+y%5E4+%2B+z%5E4+%3D+35
Can you please give me the solution as i was not able to solve it this way