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Question

Solve the following equations:
a+2x+a24x2a+2xa24x2=5xa.

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Solution

a+2x+a24x2a+2xa24x2=5xa


a+2x+a+2xa2xa+2xa+2xa2x=5xa


a+2x+a2xa+2xa2x=5xa


Applying Componendo and Dividendo

a+2xa2x=5x+a5xa

Squaring both sides

a+2xa2x=25x2+a2+10ax25x2+a210ax


a+2xa2x=(25x2+a2)+10ax(25x2+a2)10ax

Again applying Componendo and Dividendo

a2x=25x2+a210ax

a2=25x2+a210a(x0)

10a2=50x2+2a2

50x2=8a2x2=4a225

x=±2a5


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