a In the expansion of a binomial (a + b)^n the third term is equal to 56, the fourth term is , and the binomial coefficients of the third and the sixth term are equal. Find the values of a, b, and n.?
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Given:
T3 = 56/9. & T4 = 70/3
Binomial coefficient of
T3 = binomial coefficient of T6
nC2 = nC5
On solving this equation we get
(n-2)(n-3)(n-4)=60
From here we get only one real and integral solution that is
n=7. Ans
Now we will operate for the given first condition that is
T3= 56/9
nC2a(n-2) b2= 56/9
Since we found n = 7
7*6*a5b2/2 = 56/9
a5b2 =8/27 (1st eqn)
T4= 7C3a4b3 = 70/3
7*6*5 a4b3/6= 70/3
a4b3 = 2/3 (2nd eqn)
from equation 1 and 2 we get
a/b=4/9 (3rd eqn)
On solving 1st, 2nd and 3rd equation
We get
a = 2/3. & b = 3/2. Ans
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