If alpha,beta!=0 , and f(n)""=alpha^n+be...

If `alpha,beta!=0` , and `f(n)""=alpha^n+beta^n` and `{:|(3, 1+f(1),1+f(2)), (1+f(1),1+f(2),1+f(3)), (1+f(2),1+f(3),1+f(4))|:}=K(1-alpha)^2(1-beta)^2(alpha-beta)^2` , then K is equal to
(1) `alphabeta`
(2) `1/(alphabeta)`
(3) `1`
(4) `-1`

AI Generated Solution

Similar Questions

Explore conceptually related problems

Let f(n)=a^n+b^n and |(3, 1+f(1), 1f(2)),(1+f(1), 1+f(2), 1+f(3)),(1+f(2), 1+f(3), 1+f(4))|=k(1-a)^2(1-b)^2(a-b)^2 , then k= (A) 0 (B) 1 (C) -1 (D) 4

If f(x)=alpha x+beta and f(0)=f^(1)(0)=1 then f(2) =

If f(x)= alpha x+beta and f(0)=f^(')(0)=1 then f(2) =

| alpha alpha1 beta F|=(alpha-P)(beta-alpha)

If alpha+beta=1 , and alpha.beta=-(3)/(2) , then find alpha^(2)+beta^(2)=

If a+alpha=1,b+beta=2 and af(n)+alphaf(1/n)=bn+beta/n , then find the value of (f(n)+f(1/n))/(n+1/n)

If f(alpha, beta) = cos^(4)alpha/cos^(2)beta + sin^(4)alpha/sin^(2)beta then prove that f(alpha, beta) =1 ⇔ f(beta, alpha) =1 .