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In large signal analysis of differential amplifier there are some equations to determine iDS.

If we simplify it looks like that :

\$ \large 2x^2+2kx+k^2-2\frac{l}{m}=o\$

Is there an easy way to solve these kind of equations. What should one study to easily solve these kind of problems?

Edit

Original equation looks like this.

Signal analysis of differential amplifier

Citation :

Agarwal, Anant, Lang, Jeffrey. Foundations of Analog and Digital Electronic Circuits.. [edx].

Edit

Ok. I solved equation using completing the square technic.

\$ \large (x+\frac{k}{2})^2 = \frac {l} {m} - \frac{k^2}{4}\$

\$ \large x = \frac{1}{2}(\frac {\sqrt {4l-mk^2}}{\sqrt{m}} - k) \$

  • 1
    Looks like a simple quadratic equation to me (assuming x is the unknown). Grade 6 or so.... – Eugene Sh. Mar 27 '19 at 15:07
  • 2
    Algebra 101..., – Tony Stewart EE75 Mar 27 '19 at 15:23
  • I'm voting to close this question as off-topic because it's off topic. – Scott Seidman Mar 27 '19 at 19:57
  • I don't think so. Because sometimes mathematics and physics are necessary to understand theory and very useful in engineering courses. Is it possible to analyze an RC circuit without differential equations? –  Mar 27 '19 at 20:45
  • @Erdem -- there's a subtraction operation in the equation. Perhaps that should break out into it's own question?? – Scott Seidman Mar 28 '19 at 15:16
  • I am surprised to learn that most of my problem-solving problems are with mathematics rather than my understanding of theory. I try to identify the areas where I have difficulty solving the problem. Many times, my actual deficiencies are in my understanding and ability to use certain mathematical principles. For now I watch some videos about differential equations and work some example problems in that videos. Sometimes solving a Bernoulli differential equation looks easier to me rather than solving these kinds of quadratic equations. –  Mar 28 '19 at 15:36

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