Question

(x-a)^51-(x+a)^51
find x​

Answer 1

Answer:

We have to expand

(x + a)^51 – (x – a)^51

At first, (x + a)^51 = 51^C0 x^51 + 51^C1 x^50 . a + 51^C2 x^49 . a² + ...... + 51^C51 a^51

then, (x – a)^51 = 51^C0 x^51 - 51^C1 x^50 . a + 51^C2 x^49 . a² - ...... - 51^C51 a^51

When we subtract both the values i.e. (x + a)^51 – (x – a)^51 we get,

2( 51^C1 x^50 . a + 51^C3 x^48 . a³ + ...... + 51^C51 a^51)

Thus count the number of terms that is number of odd numbers up to 51.

i.e 1, 3, 5, 7, ......, 49, 51

Apply AP:

a + (n-1)d = 51

1 + (n-1)2 = 51

n = 26

So, the total numbers of terms in the expansion is 26.

Answer 2

Answer:

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