Express Q in terms of P
$$(P)\sqrt{ (P^2 - Q)/ Q} = (1 - P)/2 $$
Here's what I did - Step 1: I squared both sides - $$(P^2)(P^2 - Q)/Q = (1-P)^2 / 4 $$
Then ... $$(P^4 - P^2Q)/Q = (1-P)^2 / 4$$
Then ... $$4P^4 - 4P^2Q = Q(1-P)^2$$
Then I got stuck .. Pls help thanks !!
$\endgroup$ 22 Answers
$\begingroup$Hint: So far, your work is correct.
The goal is to isolate $Q$ on one side of the equation. The form of the equation now is $$a+ bQ=cQ$$ (here $a,b,c$ are expressions involving only $P$). So bring the two terms containing $Q$ to the same side, then factor $Q$ out of that side to get $$a=(c-b)Q$$ You should see what to do next.
$\endgroup$ $\begingroup$After the part you've done: $$4P^4 - 4P^2Q = Q(1-P)^2$$ $$\implies 4p^4=Q(1-2P+5P^2)$$ $$\implies Q=\frac{4p^4}{1-2P+5P^2}$$
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