SOLUTION: (7) Question: Solve 3 sqrt x^2 -4x+2= 3 sqrt x+2 (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. Thanks!

Question 30457: (7) Question:
Solve 3 sqrt x^2 -4x+2= 3 sqrt x+2
(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. Thanks!
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) 0, 5

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
RELATED QUESTIONS
Question: Solve: ^3 sqrt x^2-4x+2=^3 sqrt x+2 POssible Solutions: (A) 0, 5 (B)... (answered by sdmmadam@yahoo.com)

(7)Question: Solve: ^3 sqrt x^2-4x+2=^3 sqrt x+2 (a) 0,5 (b) 1/2, 5 (c) 0, 11/2... (answered by sdmmadam@yahoo.com)

(7) Question: How many solutions for x are there in this equation: sqrt x-4 - sqrt x+8... (answered by josmiceli)

(7) Solve 125x^3 -64=0 (A) -4/5, -2+2 sqrt 3i/5 (B) 4/5, -2+2 sqrt 3i?5 (C) -4/5,... (answered by mukhopadhyay)

Solve the system: x^2+y^2=63 x^2-3y^2=27 (A) (3 sqrt 6, 3) (3 sqrt 6, -3) (-3 sqrt... (answered by mukhopadhyay)

(7) Question: Solve for y: -2y-2 = sqrt 2y^2-7 -7 (You may include extraneous solutions) (answered by sdmmadam@yahoo.com)

(m) Question: ^3 sqrt 9x-4=^3 sqrt 2x+9 Answers: (a) -8/13 (b) 13/7 (c) 2 (d)... (answered by sdmmadam@yahoo.com)

(8) Question: Choose the nonlinear systesm below that have (x,y)=(4,3) as on of their... (answered by venugopalramana)

(#7) Question: Solve the system: x^2+y^2=20 x^2-2y^2=8 Answers: (A) (04,2) (-4,-2) (answered by sdmmadam@yahoo.com)