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The sum of 2 numbers is 4 (sqrt 3)   and their product is 3.

 

Determine quadratic equation which finds these two numbers

 

Then solve this equation and show that it's roots are in fact the two said numbers.

 Dec 18, 2016

Best Answer 

 #2
avatar+37146 
+5

oOOPS......here is how

 

x+y = 4 (sqrt3)

x*y = 3     so   y = 3/x  (sub this into the first equation)

 

x + 3/x = 4 sqrt3     Multiply through by 'x'

x^2 + 3 = 4 sqrt 3  x     re-arrange

x^2 - 4 sqrt3  x   + 3 = 0          Now use the quadratic formula to find   2 (sqrt 3)-3   and   2 (sqrt 3) + 3

 

Quadratic Formula:

 

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

 Dec 18, 2016
 #1
avatar+37146 
+5

2(sqrt 3) - 3     and     2(sqrt 3) +3

 Dec 18, 2016
 #2
avatar+37146 
+5
Best Answer

oOOPS......here is how

 

x+y = 4 (sqrt3)

x*y = 3     so   y = 3/x  (sub this into the first equation)

 

x + 3/x = 4 sqrt3     Multiply through by 'x'

x^2 + 3 = 4 sqrt 3  x     re-arrange

x^2 - 4 sqrt3  x   + 3 = 0          Now use the quadratic formula to find   2 (sqrt 3)-3   and   2 (sqrt 3) + 3

 

Quadratic Formula:

 

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

ElectricPavlov Dec 18, 2016

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