SOLUTION: Question: Solve: ^3 sqrt x^2-4x+2=^3 sqrt x+2 POssible Solutions: (A) 0, 5 (B) 1/2, 5 (C) 0, 11/2 (D) 1/2, 11/2 Please be specific as to which letter answer is correct

Question 30375: Question:
Solve:
^3 sqrt x^2-4x+2=^3 sqrt x+2
POssible Solutions:
(A) 0, 5
(B) 1/2, 5
(C) 0, 11/2
(D) 1/2, 11/2
Please be specific as to which letter answer is correct please
Thanks for your help!
Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
^3 sqrt x^2-4x+2=^3 sqrt x+2
Probably the question is
[sqrt (x^2-4x+2)]^3 = [sqrt (x+2)]^3 ----(1)
This implies
(x^2-4x+2) = (x+2)
x^2-4x-x+2-2 = 0 (grouping like terms)
x^2-5x = 0
x(x-5) = 0
x =0 or (x-5)=0 which gives x = 5
Answer: x = 0 or x = 5
which is your choice (A)

Let us evolve a model out of this
[sqrt(p)]^3 =[sqrt(q)]^3
[(p)^(1/2)]^3= [(q)^(1/2)]^3
[(p)^(3/2)]= [(q)^(3/2)] (using [(a)^m]^n =[(a)^(mn) ——(*)] )
Now raising both the sides to the power (2/3)
[(p)^(3/2)]^(2/3)= [(q)^(3/2)]^(2/3)
{(p)^[(3/2)X(3/2)]}= {(q)^[(3/2)X(3/2)]}
[(p)^1]= [(q)^1] ((using (*) )
That is p = q
Note: The above steps if we go through repeatedly then
we will be in a position to just observe and conclude
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