SOLUTION: Kindly help me solving it i tried my best but I couldn't Solving equation {{{(x+(12p-x)^(1/2))/(x-(12p-x)^(1/2))=(p^(1/2)+1)/(p^(1/2)-1)}}} following roots are obtained I ttied

Algebra ->  Radicals -> SOLUTION: Kindly help me solving it i tried my best but I couldn't Solving equation {{{(x+(12p-x)^(1/2))/(x-(12p-x)^(1/2))=(p^(1/2)+1)/(p^(1/2)-1)}}} following roots are obtained I ttied      Log On


   

Question 1046395: Kindly help me solving it i tried my best but I couldn't
Solving equation following roots are obtained
I ttied it this way
Let us assume that %2812p-x%29%5E%281%2F2%29=aand p%5E%281%2F2%29=b
So the reformed equation will be
%28x%2Ba%29%2F%28x-a%29=%28b%2B1%29%2F%28b-1%29
By cross multiplication we get
%28x%2Ba%29%28b-1%29=%28x-a%29%28b%2B1%29
Or xb-x%2Bab-a=xb%2Bx-ab-a
Or 2x-2ab=0
Taking two as common factor
x-ab=0
Or x=ab
By putting the values it becomes
x=%2812p%5E2-px%29%5E%281%2F2%29
But thag is not the correct answer
Please help Me by showing the correct steps
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
From x=%2812p%5E2-px%29%5E%281%2F2%29,
===> x%5E2=+12p%5E2-px, after squaring both sides.
===> x%5E2%2Bpx+-+12p%5E2+=+0,
===> (x+4p)(x-3p) = 0
===> x = -4p or 3p.
Direct substitution of highlight%28x+=+3p%29 into the original equation proves that it is a solution.
Direct substitution of x = -4p into the original equation proves that it is an extraneous solution.