Question

if an+bn/an-1+bn-1
be AM between two numbers
a and b', then find 'n ?​

Answer 1

Answer:

n=1

Step-by-step explanation:

a^n+b^n/a^n-1+b^n-1

we know that mean of a and b,A.M=a+b/2

a^n+b^n/a^n-1+b^n-1=a+b/2

2a^n+2b^n=(a^n-1+b^n-1)(a+b)

a^1.a^n-1+ba^n-1+b^1.b^n-1=2a^n+2b^n

ab^n-1+ba^n-1=2a^n+2b^n-a^n+b^n

ab^n-1-b^n=a^n-ba^n-1

b^n-1(a-b)=a^n-1(a-b)

both (a-b) are cut then

b^n-1=a^n-1

b^n-1/a^n-1=1

(b/a)^n-1=(b/a)^0

Power of LHS=RHS

n-1=0

then,n=1