Wednesday, September 14, 2011

EQUATION SOLVING METHOD


x2 + 2x + 7             x + 2
__________ =        _____
x2+ 3x + 5               x + 3

In the conventional method we proceed as
x2 + 2x + 7             x + 2
__________ =       _____
x2 + 3x + 5             x + 3

(x + 3) (x2 + 2x + 7) = (x + 2) (x2 + 3x + 5)
x3 + 2x2 + 7x + 3x2 + 6x + 21 = x3 + 3x2 + 5x + 2x2 + 6x + 10
x3 + 5x2 + 13x + 21 = x3 + 5x2 + 11x + 10

Canceling like terms on both sides
13x + 21 = 11x + 10
13x – 11x = 10 – 21
2x = -11
x = -11 / 2


Now we solve the problem using anatyayoreva formula.
x2 + 2x + 7          x + 2
__________ =     _____
x2 + 3x + 5         x + 3


Consider
x2 + 2x + 7              x + 2
__________ =           _____
x2+ 3x + 5               x + 3

Observe that
x2 + 2x             x (x + 2)                     x + 2
______ =          ________         =      _____
x2+ 3x              x (x + 3)                     x + 3

This is according to the condition in the sutra. Hence from the sutra
x + 2              7
_____    =     __
x + 3              5

5x + 10 = 7x + 21
7x – 5x = -21 + 10
2x = -11
x = -11 / 2

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