if x+y +z =1 X^2+Y^2+Z^2=2 X^3+Y^3+Z^3=3 then find  x^4 +y^4 +z^4=? use algebra

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You need to use mathematical induction, hence, you need to start with the first step of the method, the basis, such that:

`{(x + y + z = 1),(x^2 + y^2 + z^2 = 2),(x^3 + y^3 + z^3 = 3):}`

Taking the next step requires you to prove that if the statement holds for each n, hence, it also holds for `n + 1` , such that:

`x^n + y^n + z^n = n => x^(n+1) + y^(n+1) + z^(n+1) = n+1`

You need to multiplicate by x the valid statement `x^n + y^n + z^n = n` , such that:

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