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Question
If x=a−ba+b+c+d=b−ca+b+c+d=c−da+b+c+d=d−aa+b+c+d, then find x3
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Solution
x=a−ba+b+c+d(1)x=b−ca+b+c+d(2)x=c−da+b+c+d(3)x=d−aa+b+c+d(4)by(1)&(2)a−ba+b+c+d=b−ca+b+c+da−b=b−ca−2b=−ca=2b−cc−d=d−ac−2d=−aa=2(2c−d)−c=4c−2d−c=4(2d−a)−2d−c=8d−4a−2d−ca=6d−4a−c5a=6d−ca=15(6d−c)b=2c−db−c=c−db−2c=−bb=2c−dc=2d−ac=2d−65d+c54c5=2d−6d54c5=4d5c=dx=a−bb=2d−0b=da=b=c=dx=a−ba+b+c+dx=0x3=0
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