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What is $\alpha$ and $\beta$ ?

$$\frac{\alpha}{(\beta^2+1)^{3/2}}=12$$ $$\frac{\alpha}{(\beta^2+0.06^2)^{3/2}}=10$$

Thank you very much for your time.

ferahfeza
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  • Divide the two LHS and solve first the founded equality for $\beta$. –  Mar 14 '14 at 20:54

1 Answers1

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There is no real root. If there were, $\alpha$ would have to be positive. And it is clear that for positive $\alpha$ and real $\beta$, the left-hand side of the second equation is greatr than the left-had side of the first.

André Nicolas
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  • thank you very much for your hint. – ferahfeza Mar 14 '14 at 21:07
  • You are welcome. You can solve for $\beta^2$ by dividing, cubing, and simplofying. You will get a cubic in $\beta^2$. This can be solved numerically (the Cardano formula is not practical). There will be one real solution for $\beta^2$, but it will be negative. – André Nicolas Mar 14 '14 at 21:13