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Question

If x=aba+b+c+d=bca+b+c+d=cda+b+c+d=daa+b+c+d, then find x3

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Solution

x=aba+b+c+d(1)x=bca+b+c+d(2)x=cda+b+c+d(3)x=daa+b+c+d(4)by(1)&(2)aba+b+c+d=bca+b+c+dab=bca2b=ca=2bccd=dac2d=aa=2(2cd)c=4c2dc=4(2da)2dc=8d4a2dca=6d4ac5a=6dca=15(6dc)b=2cdbc=cdb2c=bb=2cdc=2dac=2d65d+c54c5=2d6d54c5=4d5c=dx=abb=2d0b=da=b=c=dx=aba+b+c+dx=0x3=0

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