The first three terms of the binomial expansion of (2 – ax)" are 64 – 16bx +100bx?. Find the value of each of the integers n, a and b.

Ans: n=6, a=5, b=60

n = 6, a = 5, b = 60

Step-by-step explanation:

In a binomial function (a + b)ⁿ expression that represents the terms,

(a + b)ⁿ =

By this formula,

1st term = = aⁿ

2nd term = =

3rd term = =

For the binomial expansion initial 3 terms of (2 - ax)ⁿ = 64 - 16bx + 100bx²

Terms of (2 - ax)ⁿ =

                             =

Comparing the terms of both the expansions,

1st term

2ⁿ = 64

2ⁿ = 2⁶

n = 6

2d term

192a = 16b

b = 12a -----(1)

3rd term

240a² = 100b

b = 2.4a² -----(2)

From equation (1) and (2),

b = 12a = 2.4a²

a =

From equation (1)

b = 12a = 60

Therefore, n = 6, a = 5, b = 60

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,