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2015-10-24T14:24:23+08:00

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Length ⇒ x
Width ⇒ x -2
Height ⇒ x - 1
Volume = 60 cubic meters

Length × Width × Height = Volume
(x) (x-2) (x -1) = 60
x³ - 3x² + 2x = 60
x³ - 3x² + 2x - 60 = 0

(x - 5) (x² + 2x + 12) = 0

x - 5 = 0
x = 5

Solve the quadratic equation x² + 2x + 12 by either Completing the Square or Quadratic Formula:

By Completing the square:
a
x² + bx + (b/2)² = c + (b/2)²

x² + 2x + (2/2)² = - 12 + (2/2)²
x² + 2x + 1 = -11 + 1
x² + 2x + 1 = -11

(x + 1) (x + 1) = -11
(x + 1 )² = -11

 \sqrt{(x + 1) ^{2} } =  \sqrt{-11}

 \sqrt{-11} is an imaginary number
 \sqrt{-11} =i \sqrt{11}
x +1 - 1 = -1 +i \sqrt{11}
x+1-1 = -1-i \sqrt{11}

Therefore the roots (x) are:
x = 5

x = -1+i \sqrt{11}
x =-1-i \sqrt{11}

Choose the positive number 5.  The dimensions are:
Length, x ⇒
5 meters
Width, x - 2 ⇒ 5 - 2 = 3 meters
Height, x - 1  ⇒ 5 - 1 = 4 meters

To check:
(5 meters) × (3 meters) × (4 meters) = 60 cubic meters

60 cubic meters = 60 cubic meters


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