SOLUTION: (m) Question: 3 sqrt 9x-4 =3 sqrt 2x+9 (A) -8/13 (B) 13/7 (C) 2 (D) -7/13 Thank you very much!

Question 30462: (m) Question: 3 sqrt 9x-4 =3 sqrt 2x+9
(A) -8/13
(B) 13/7
(C) 2
(D) -7/13
Thank you very much!
Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
The problem may be as follows:
[sqrt (9x-4)]^3 =[sqrt (2x+9)]^3 ----(1)
This implies (9x-4) = (2x+9)
(how? see the model below for you to learn and understand.
You need not show those steps if the above problem
is a 1 mark question!)
9x-2x= 9+4
7x= 13
x = 13/7
Answer: x = 13/7
which is choice (B) 13/7

Note: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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