In the expansion of `(3-sqrt(17/4+3sqrt2))^15` the 11th term is a

Options

A. an irrational number
B. a rational number
C. a positive integer
D. a negative integer

Answer

A

Explanation

We have,
`17/4 + 3sqrt(2) = 1/4 (9+8+12sqrt(2)) = 1/4 (3+2sqrt(2))^(2)`
`3-sqrt(17/4+3sqrt(2)) = 3-1/2(3+2sqrt(2)) = 3/2- sqrt(2)`
Hence, the 10 th term of `(3- sqrt(17/4 + 3sqrt(2)))^(20) = (3/2-sqrt(2))^(20) ` is
`.^(20)C_(9)(3/2)^(20-9) (-sqrt(2))^(9)`
Which is in irrational number.