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The surface area of a sphere in terms of \(\pi\) is 3364\(\pi\). the radius of the sphere is \(5x^2-7x+1\). Find x.

 Jan 13, 2024
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Surface area =  4pi *radius^2

 

3364 pi  = 4 pi (5x^2 - 7x + 1)^2

 

3364  / 4  =  (5x^2 -7x + 1)^2

 

841 = (5x^2 -7x + 1)^2 

 

Take the positive sqrt  of  both sides   ....the negative sqrt leads to a discrminant < 0

 

29 = 5x^2 - 7x + 1

 

5x^2 - 7x - 28   = 0

 

Q Formula   leads to

 

x =   ( 7 + sqrt [ 49 + 20*28 ] ) / 10  =   [ 7 + sqrt (609) ] /  10   ≈  3.168

 

 

cool cool cool

 Jan 13, 2024

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