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# Algebraic equation with square root and power

Posted 11 years ago
 (1-t) / (sqrt(1+t^2))*(sqrt(2)) = 0.5the result is t=2-sqrt(3), but i'm not able to have it !
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Posted 11 years ago
 Hi, Using proper (capitalized) function names, and If the sqrt(2) is in the denominator as i MISREAD  the first time, then I am able to get the solution presented with the question.(* The following form has the proposed solution. *)Solve[ (1-t)/(Sqrt[(1+t^2)] Sqrt[2])==(1/2), t]{{t -> 2 - Sqrt[3]}}(* The question as presented has the solutions shown by Thiel. *)I think its easy to mis-read the brackets when the equation is in the in-line form.
Posted 11 years ago
 Dear Charles,please do type it into Wolfram alpha or click on this link:http://www.wolframalpha.com/input/?i=%281-t%29+%2F+%28sqrt%281%2Bt%5E2%29%29*%28sqrt%282%29%29+%3D%3D+0.5Once you see the result click on "step-by-step" solution. For your convenience I have attached the notebook that wolfram alpha generates.M. Attachments:
Posted 11 years ago
 I'm trying to understand where i made a mistake, do you have a step by step solution to propose ?
Posted 11 years ago
 Hi,there are some parenthesis that need to be changed and Sqrt is capitalised.Solve[(1 - t)/(Sqrt[1 + t^2])*(Sqrt[2]) == 1/2, t]gives{{t -> 1/7 (8 - Sqrt[15])}}or {{t -> 0.589574}}which is different from your solution. In fact, your suggested solution does not appear to solve the equation:In[90]:= (1 - t)/(Sqrt[1 + t^2])*(Sqrt[2]) == 1/2 /. t -> 2 - Sqrt[3]Out[90]= FalseIn[93]:= (1 - t)/(Sqrt[1 + t^2])*(Sqrt[2]) == 1/2 /.   t -> 1/7 (8 - Sqrt[15]) // NOut[93]= TrueM.