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Question

If x=2a+1+2a12a+12a1, then show that x24ax+1=0

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Solution

x=2a+1+2a12a+12a1=(2a+1+2a1)(2a+12a1).(2a+1+2a1)(2a+1+2a1)=(2a+1+2a1)22a+12a+1=2a+1+2a1+2(2a+1)(2a1)22x=4a+2(2a)21x=2a+4a21x2a=4a21(x2a)2=4a21x2+4a24ax=4a21x24ax+1=0

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