1.

The sum of the coefficients of all even degree terms is x in the expansion of (x + sqrt(x^(3) - 1))^(6) + (x - sqrt(x^(2) - 1))^(6), (x gt 1) is equal to

Answer»

29
32
26
24

Solution :Use formula
`(a + b)^(N) + (a - b)^(n) =`
`2[.^(n)C_(0) a^(n) + .^(n)C_(2) a^(n - 2) b^(2) + .^(n)C_(4) a^(n - 1) b^(4)` + …… 1
Given expansion is `(x + SQRT(x^(3) - 1))^(6) + (x - sqrt(x^(3) - 1))^(6)`
`= 2[.^(6)C_(0) x^(6) + .^(6)C_(2) x^(4) (sqrt(x^(2) - 1))^(2)`
`{ :' (a + b)^(n) + (a - b)^(n)`
`= 2 [.^(n)C_(0) a^(n) + .^(n)C_(2) a^(n - 2) b^(2) + .^(n)C_(4)a^(n - 4) b^(4) + ...]}`
The SUM of the terms with EVEN power of x.
` 2[.^C_0x^6+.^C_2(-x^4)+.^6C_4x^8+.^6C_4x^2+.^6C_6(-1-3x^6)]`.
` =2[.^6C_0x^6-.^6C_2x^4+.^6C_4x^8 +.^6C_4x^2-1 -3x^6]`
Now, the required sum of the coefficient of even powers of x in
`(x+sqrt(x^3-1))^6+(x-sqrt(x^3-1))^6`
` =2[.^6C_0-.^6C_2+.^6C_4+.^6C_4-1-3]`
` =2[1-15+15+15-1-13]=2(15-3]=2(15-3)=24`


Discussion

No Comment Found

Related InterviewSolutions