Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

hey my lecturer put this example up for an exam tomorrow, could someone please explain how he gets to the 3rd line? is he using factorization?

$$V_{\mathrm{dsb}}=V_{\mathrm{gsb}}-V_{\mathrm t}$$

$$V_{\mathrm{dsb}}=V_{\mathrm{dd}}-(R_{\mathrm d}/2)K_n(V_{\mathrm{gsb}}-V_{\mathrm t})^2$$

$$V_{\mathrm{gsb}}=V_{\mathrm t}+(\sqrt{2K_{\mathrm n}R_{\mathrm d}V_{\mathrm{dd}}+1}-1)/K_{\mathrm n}R_{\mathrm d}$$

share|improve this question
    
I'm sorry, but your equation is unreadable right now. I'm guessing some of the letters are supposed to be subindices. Are the variables supposed to be $V_{dsb}$, $V_{dd}$, $R_d$, $K_n$, $V_{gsb}$, and $V_t$? –  Arturo Magidin Sep 22 '11 at 13:16
    
I formatted the equations. It was rather non-trivial to guess what you meant; please check that everything is as it should be. You can right-click on the equations and select "Show Source" to see how to do the formatting so you can do it yourself next time. –  joriki Sep 22 '11 at 13:28

1 Answer 1

The first equation states that the expression being squared in the second equation is $V_{\mathrm{dsb}}$. Thus the second equation becomes

$$V_{\mathrm{dsb}}=V_{\mathrm{dd}}-(R_{\mathrm d}/2)K_nV\;_{\mathrm{dsb}}^2\;.$$

This is a quadratic equation for $V\;_{\mathrm{dsb}}$. Substituting one of its two solutions into the first equation yields the third equation.

share|improve this answer
    
sorry about the formatting, thanks for the help it just wasn't clicking, and thanks for the formatting help –  michael Sep 22 '11 at 14:05

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.