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Question

If (1+x)10=a0+a1x+a2x2+......a10x10, then value of
(a0a2+a4a6+a8a10)2+(a1a3+a5a7+a9)2 is

A
210
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B
2
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C
220
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D
None of these
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Solution

The correct option is B None of these
x=i
(1+i)10=a0+a1ia2a3i+a4......a10 ……….(1)
x=i
(1i)10=a0a1ia2+a3i+a4.....a10 ……..(2)
(1) + (2)
(1+i)10+(1i)10=2(a0a2+a4......a10)
(2)10((eiπ/4)10+(eiπ/4)10)=2(a0+a2+a4....)
25=2(a0a1...)
(a0+a2+a4......a10)2=0
(1) - (2)
(1+i)10(1i)10=(a1a3+a5.....an)i
(2)10 (2sin10π4)i=(a1a3+a5.....a9)i
(26)2=(a1a3+a5.....a9)2=212
(a0a2+a4.....a10)2+(a1a3+a5...+a9)2=212.

1093279_1156153_ans_2e2269b9fb874175b63f169d47ed6401.jpg

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