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Question

Let D1=∣ ∣aba+bcdc+dabab∣ ∣,D2=∣ ∣aca+cbdb+daca+b+c∣ ∣, then the value of D1D2, where b0 and adbc, is ............

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Solution

Given D1=∣ ∣aba+bcdc+dabab∣ ∣
D1=∣ ∣abacdcaba∣ ∣+∣ ∣abbcddabb∣ ∣
D1=∣ ∣abbcddabb∣ ∣
C2C2C3
D1=∣ ∣a0bc0da2bb∣ ∣
D1=2b(adbc) .....(1)
D2=∣ ∣aca+cbdb+daca+b+c∣ ∣
D2=∣ ∣acabdbaca∣ ∣+∣ ∣accbddacb+c∣ ∣
D2=∣ ∣accbddacb+c∣ ∣
C2C2C3
D2=∣ ∣a0cb0dabb+c∣ ∣
D2=b(adbc) .....(2)
D1D2=2 (by (1) and (2) )

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