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Question

If (1+x+x2)8=a0+a1x+.....a16x16 then a0a2+a4a6+.....+a16=

A
1
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B
2
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C
3
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D
4
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Solution

The correct option is A 1
Putting x=i
(1+i+i2)8=a0+a1i+a2i2+.....+a16i16
(i)8=a0+a1ia2+....(1)
putting x=i
(1i+(i)2)8=a0a1i+a2(i)2+.....
(i)8=a0a1ia2+.........(2)
equation (1)+ equation (2) i8+i8=2(a0a2........)
2=2(a0a2.....)
a0a2.......1 (A)


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