# Math Help - Transposition of a formula

1. ## Transposition of a formula

Hello everyone,

I didn't know how to proceed with the following question:

Given $q = \sqrt{(5p^2 - 1)^2 -2}$ find $p$ in terms of $q$

I started off by squaring both sides, which I am pretty sure is the right thing to do, but I still can't figure out how to get p on its own on the left hand side.

In the back of the book the answer is $p = \sqrt{\frac{\sqrt{q^2 + 2} + 1}{5}}$

I tried to work backwards from this, but I still can't figure it out. Any help would be appreciated.

Regards,

evanator

2. $q^2=(5p^2-1)^2-2$

$q^2+2=(5p^2-1)^2$

$5p^2-1=\pm\sqrt{q^2+2}$

$p^2=\frac{\pm\sqrt{q^2+2}+1}{5}$

$p=\pm\sqrt{\frac{\pm\sqrt{q^2+2}+1}{5}}$

3. Thanks!