Question
Question: If (1 + x)<sup>10</sup> = a<sub>0</sub> + a<sub>1</sub>x + a<sub>2</sub>x<sup>2</sup> + .... +a<sub>...
If (1 + x)10 = a0 + a1x + a2x2 + .... +a10x10, then
(a0 – a2 + a4 – a6 + a8 – a10)2 + (a1 – a3 + a5 – a7 + a9)2 is equal to –
A
310
B
210
C
29
D
None of these
Answer
210
Explanation
Solution
Putting x = i, –i and multiplying both the results, we get the value of the required expression as,
(a0 – a2 + a4 – a6 + a8 – a10)2 + (a1 – a3 + a5 –a7 + a9)2
= (1 + i)10 (1 – i)10 = (1 + 1)10 = 210.