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Grade: 12th pass
        
If(1+x+x^2)^8=a0+a1x+.....+a16x^16 then a1-a3+a5-a7+.......-a15=
3 months ago

Answers : (1)

Aditya Gupta
1716 Points
							
hello oleti. this is an ez application of complex nos:
given that (1+x+x^2)^8=a0+a1x+.....+a16x^16
multiply both sides by x
x(1+x+x^2)^8=a0x+a1x^2+a2x^3+a3x^4.....+a16x^17
now, in this identity, put x= iota
i(1+i+i^2)^8= a0*i – a1 – a2*i + a3+a4*i – …......+a16i.......(1)
now put x= – iota
 – i(1 – i+i^2)^8= – a0*i – a1+a2*i+a3 – a4*i – …........ – a16i......(2)
add (1) and (2)
i(1+i+i^2)^8 – i(1 – i+i^2)^8= – 2(a1 – a3 + a5 – …....... – a15)
or i*i^8 – i*i^8= – 2(a1 – a3 + a5 – …....... – a15)
0= – 2(a1 – a3 + a5 – …....... – a15)
or a1-a3+a5-a7+.......-a15= 0
kindly approve :)
3 months ago
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