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Question

Solve:
∣ ∣ ∣a2+1abacabb2+1bccacbc2+1∣ ∣ ∣=1+a2+b2+c2

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Solution

Now we have
=abc∣ ∣ ∣ ∣ ∣ ∣a+1aaabb+1bbccc+1c∣ ∣ ∣ ∣ ∣ ∣=a2b2c2∣ ∣ ∣ ∣ ∣ ∣1+1a21111+1b21111+1c2∣ ∣ ∣ ∣ ∣ ∣=a2b2c2{(1+1a2)(1+1b2)(1+1c2)1(1+1c21)+(111b2)}=a2b2c2[(1+1a2){1+1c2+1b2+1b2c21}1c21b2]=a2b2c2(1c2+1b2+1b2c2+1a2c2+1a2b2+1a2b2c21c2b2)=a2b2+a2c2+a2+b2+c2+1a2b2a2c2hence,weget=a2+b2+c2+1

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