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Chaos_Enlightened
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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]
Chaos_Enlightened said:Got x^3-6x^2+12x=14+6(2^1/3+2^2/3)
Nidum said:Hint : work out the numerical value of x from the first equation .
What do you do then ?
Hello Chaos_Enlightened. Welcome to PF !Chaos_Enlightened said: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...Delta² said:##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) \ ?##Chaos_Enlightened said: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
SammyS said: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:Sahil Kukreja said:Yes, that's what i was saying in post #16.
I see that I missed that post of yours.Sahil Kukreja said:Your question is wrong. it should be :- x= 2 + 2^(1/3) + 2^(2/3)
otherwise your calculations are wrong, you can just check.
SammyS said: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}\ ? ##
Algebraic manipulation involving powers is the process of rearranging and simplifying equations that contain variables raised to various powers.
Algebraic manipulation involving powers is important because it allows us to solve for unknown variables and simplify complex equations in various fields of science and mathematics.
Some common techniques include factoring, expanding, and using the laws of exponents such as the product rule, quotient rule, and power rule.
Yes, algebraic manipulation involving powers can be used in real-life situations such as calculating compound interest, determining growth rates, and analyzing data in scientific experiments.
Some tips include practicing basic algebraic operations, understanding the rules of exponent and logarithmic functions, and breaking down complex equations into smaller, more manageable steps.