Question #c0b35

2 Answers
Sep 13, 2016

The Soln. is : (1) : x=(p^2+3pq+4q^2)/(p+3q), if p+3qne0.

(2) : If p+3q=0, i.e., p=-3q rArr q=0", & the soln. is, "x=0

Explanation:

I have to add a little to the Answer submitted by Respected

Dr. Cawas K.

Dr.'s soln. is x=(p^2+3pq+4q^2)/(p+3q).

This soln. is based upon the assumption that p+3q!=0

So, out of curiosity, I tried to see what happens to the Soln. if,

p+3q=0, or, p=-3q And, here is the Result :

Letting p=-3q, in the eqn., we get,

sqrt(x+3q)+sqrt(x-q)=(p+q)/sqrt(x-q)=(-2q)/sqrt(x-q)

:. sqrt((x+3q)(x-q))+x-q=-2q, or,

sqrt((x+3q)(x-q))=-q-x.

Squaring, (x+3q)(x-q)=(-q-x)^2

:. x^2+2qx-3q^2=q^2+2qx+x^2, or, -4q^2=0 rArr q=0

Thus, p=-3q rArr q=0 rArr p=0.

Hence, in case, p=-3q=0, the eqn. becomes,

sqrtx+sqrtx=0 rArr x=0.

Thus, the Soln. is : (1) : x=(p^2+3pq+4q^2)/(p+3q), if p+3qne0.

(2) : If p+3q=0, i.e., p=-3q rArr q=0", & the soln. is, "x=0

Sep 14, 2016

With x>p and x>q..
p+1, when p=q.
p+q, including 2p, when p=q..

Explanation:

I have learnt there is a typographical error in the equation and the

correct equation is

sqrt (x-p)+sqrt (x-q)=p/sqrt (x-q)+q/sqrt (x-p), x> both p and q.

Rearranging,

sqrt (x-p)-q/sqrt (x-p)=p/sqrt (x-q)-sqrt (x-q)

Upon squaring.

x-p+q^2/(x-p)-2q=p^2/(x-q)+x-q-2p. Upon simplfiication,

(p-q)(x-p)(x-q)=p^2(x-p)-q^2(x-q).

(p-q)(x^2-2(p+q)x+(p^2+q^2+2pq)=0

p-q=0 and/or x^2-2(p+q)x+p^2 + q^2 +2pq=0

The zeros of the quadratic are

x = p+q, p+q.,

So, the list is

x=p+1, when p=q

x=p+q, including 2p, when p=q.

I think there are no bugs now, and this is my final edition.
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