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Homework Statement
If x=2+2^1/2+2^2/3. Then x^3-6x^2+6x=?
Homework Equations
(A+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca+)
The Attempt at a Solution
x^2= 6+3(2^2/3)+2^4/3+4(2^1/3)[/B]
Got x^3-6x^2+12x=14+6(2^1/3+2^2/3)
Hint : work out the numerical value of x from the first equation .
What do you do then ?
Hello Chaos_Enlightened. Welcome to PF !Homework Statement
If x=2+2^1/2+2^2/3. Then x^3-6x^2+6x=?
I don't think that it factorizes any more than that at least in integers. I could be wrong though it would not be the first time...##x^3-6x^2+6x=x(x^2-...+...)## the polynomial inside the parenthesis is a 2nd order polynomial i believe you know how to factorize it,
Where did you get ##\ 6\left(2^{1/3}+2^{2/3}\right) \ ?##Wait
I could just substitute then
x^3-6x^2+12x=14+6(2^1/3+2^2/3). ==:
x^3-6x^2+12x=14+6x-12. ==:
Ans. Is 2
Where did you get ##\ 6\left(2^{1/3}+2^{2/3}\right) \ ?##
... or should the original problem state that ##\ x=2+2^{1/3}+2^{2/3}\ ## rather than ##\ x=2+2^{1/2}+2^{2/3}\ ? ##
Post #16:Yes, that's what i was saying in post #16.
I see that I missed that post of yours.Your question is wrong. it should be :- x= 2 + 2^(1/3) + 2^(2/3)
otherwise your calculations are wrong, you can just check.
Where did you get ##\ 6\left(2^{1/3}+2^{2/3}\right) \ ?##
... or should the original problem state that ##\ x=2+2^{1/3}+2^{2/3}\ ## rather than ##\ x=2+2^{1/2}+2^{2/3}\ ? ##