+289 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.
+128664 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
