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Question

Find the value of (214−1)(234+212+214+1).


A

2

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B

-1

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C

-2

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D

1

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Solution

The correct option is D

1


Putting214=x,weget:(2141)(234+212+214+1)=(x1)(x3+x2+x+1),wherex=214=(x1)[x2(x+1)+(x+1)]=(x1)(x+1)(x2+1)=(x21)(x2+1)=(x41)=[(214)41]=[2(14×4)1]=(21)=1.


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