SOLUTION: (m) Question: ^3 sqrt 9x-4=^3 sqrt 2x+9 Answers: (a) -8/13 (b) 13/7 (c) 2 (d) -7/13 Please be specific as to which letter answer is correct. thanks for your help!

Question 30479: (m) Question:
^3 sqrt 9x-4=^3 sqrt 2x+9
Answers:
(a) -8/13
(b) 13/7
(c) 2
(d) -7/13
Please be specific as to which letter answer is correct. thanks for your help!
Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
^3 sqrt 9x-4=^3 sqrt 2x+9
Probably the question is
[sqrt(9x-4)]^3 = [sqrt(2x+9)]^3
This means [(9x-4)^(1/2)]^3 = [(2x+9)^(1/2)]^3 (as sqrt(p) means (p)^(1/2) )
[(9x-4)^(3/2)]= [(2x+9)^(3/2)] (using [(a)^m]^n =[(a)^(mn) ----(*)]
Now raising both the sides to the power (2/3)
[(9x-4)^(3/2)]^(2/3)= [(2x+9)^(3/2)]^(2/3)
{(9x-4)^[(3/2)X(3/2)]}= {(2x+9)^[(3/2)X(3/2)]} (using (*) )
That is (9x-4)^1 = (2x+9)^1
That is (9x-4) = (2x+9)
9x-2x= 9+4 (grouping like terms)
7x = 13
x = 13/7
Answer: x = (13/7)
which is your choice (b)
Note: If you can feel the nerve of the problem the idea behind it is very simple and you can see it in your mental eye.
Keep staring at the steps and absorb the concept!

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