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Question

Solve the following equation by using the method of completing the square:
x24x+1=0

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Solution

The difference of squares identity can be written:
A2B2=(AB)(A+B)
We can complete the square and use this with as follows:
x24x+10=0
x24x+430=0
(x2)2(3)20=0
((x2)3)((x2)+3)=0
(x23)(x2+3)=0
Hence:x=2±3



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