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Let u and v be the solutions to 3x^2 + 5x = 7 = 0. Find u^2 + v^2.

 Jan 9, 2022
 #1
avatar+28 
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I'm assuming that by "3x^2+5x=7=0" you mean 3x^2+5x-7=0. Because this quadratic isn't easily factorable (or solvable via the difference of squares), we can use the quadratic formula. Through the quadratic formula, we find that the solutions to the equation are (-5+sqrt{109})/6 and (-5-sqrt{109})/6. Squaring both expressions gives (67-5sqrt{109})/18 and (67+5sqrt{109})/18. The square roots cancel out, which gives 134/18, simplifying to 67/9.

 Jan 9, 2022
 #2
avatar+36453 
+1

3x^2 + 5x + 7 = 0     ( I assume the '+' sign....it is the same key on my keyboard)

 

By Vieta's Formulas  

   u+ v = -5/3     and   uv = 7/3

 

(u+v)^2 =

                u^2 + v^2        + 2 uv    = (-5/3)^2

                u^2 + v^2                      =    25/9   - 2uv

                u2  +  v2                       =  25/9  - 2(7/3) =  -17/9 =  - 1.8888888.....

 Jan 10, 2022

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