Question 374088
The sum of the area s of two circles is 65pi square feet. The length of a radius of the larger circle is one foot less than twice the length of the radius of the smaller circle. Find the length of a radius of each circle.

Sol'n:
  let R - radius of big circle
      r - radius of small circle
  A1+A2 = 65pi
   R^2pi + r^2pi = 65pi, eliminating pi on both side
   R^2 + r^2 = 65 ----(1)
   R = 2r-1 -----(2)
 substitute (2)into (1),
 (2r-1)^2 + r^2 = 65
  4r^2 - 4r + 1 r^2 = 65
  5r^2 - 4r - 64 = 0, factor then equate to zero to find the value of r.
  r = 4---acceptable
  r = -3.2----absurd,
 thus,
  r = 4 ft.          -----ans.
  R = 2(4)-1 = 7 ft. -----ans.