The value of ∣∣
∣∣x+42x2x2xx+42x2x2xx+4∣∣
∣∣,x∈R−{−45,4} is
A
(5x+4)(4−x)
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B
(5x−4)(4−x)2
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C
(5x+4)(4−x)2
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D
(5x+4)(4−x)3
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Solution
The correct option is C(5x+4)(4−x)2 Applying C1→C1+C2+C3,
We get, Δ=∣∣
∣∣5x+42x2x5x+4x+42x5x+42xx+4∣∣
∣∣=(5x+4)∣∣
∣∣12x2x1x+42x12xx+4∣∣
∣∣
Now applying R2→R2−R1,R3→R3−R1
We get, Δ=(5x+4)∣∣
∣∣12x2x04−x0004−x∣∣
∣∣=(5x+4)(4−x)2