Question

Number of irrational terms in the expansion of (√2 + √3 )^15 is equal to
(A) 16
(C) 12
(D) 15
(B) 7

plz provide soln too​

Answer 1

Answer:

Number of irrational terms in the expansion of (√2 + √3 )¹⁵ is  16

Step-by-step explanation:

as we know that

(a + b)ⁿ   = aⁿ  + ⁿC₁aⁿ⁻¹b¹  + ⁿC₂aⁿ⁻²b² +.......................................+ ⁿCₙ₋₁a¹bⁿ⁻¹ + bⁿ

a = √2

b = √3

n = 15

For even powers of √2  & √3  number would be rational

xth  Term  = ⁿCₓaⁿ⁻ˣbˣ   where x is from 0 to 15

number to be rational

n-x   &  x  both should be even

n = 15

15 -x   &  x  both should be even

No such value of x exist

as 15-x + x  = 15  (odd number  , while sum of two even numbers = even numbers)

Hence no rational number exists

Hence All 16 terms are irrational

Number of irrational terms in the expansion of (√2 + √3 )¹⁵ is  16